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Equation for compounded interest?
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Equation for compounded interest?
Period can be months, quarters, years, etc. With simple interest, we were assuming that we pocketed the interest when we received it. To calculate interest compounded daily, just use the daily compound interest formula A = P(1 + r / 365) 365t In the formula, just divide the interest rate by 365 and multiply t or the number of years by 365. Step 2: Contribute. Jun 16, 2024 · The future value formula using compounded annual interest is: FV = PV⋅(1 + r) n. The formula for compound interest is defined as: where: S = Final Dollar Value. Determine the annual interest rate (r) and convert it to a decimal format. The number of compounding periods is equal to the term in years multiplied by the corresponding factor. Frequently Asked Questions. The first compound telescope was made b. Compound Interest with Regular Contributions Formula. You can also calculate your total interest using the compound interest formula from above: Total Interest Payable After Three Years = $ 78 , 812. 50 , or $ 500 , 000. By doing so, we can better understand the difference between simple and compound interest. The formula for continuous compound interest is given by the equation A = P * e^ (rt), where: A is the amount of money accumulated after n years, including interest. n = Number of Compounding Periods. Which of the following is a true statement? a. The formula for calculating compound interest is: A = P(1 + r/n)^(nt) Where: - A is the future value of the investment or loan, including both principal and interest - P is the principal amount (initial investment or loan amount) - r is the annual interest rate (expressed as a decimal) - n is the number of times interest is compounded per year Substituting into the continuous compound interest formula: \[A=Pe^{rt}=20000e^{005\] Thus the college saving account has grown from $20,000 to $40,275. In the formula, A represents the final amount in the account that starts with an initial P using interest rate r for t years. If we start the year with $100 and compound only once, at the end of the year, the principal grows to. 28, which is only $0. For example, the compound interest formula for compounded monthly would be CI = P (1 + r/12) 12t - P. t = Investment Time in Years. She wanted to pay off a loan within 5 years, and they wanted us to find the interest she paid off. Using algebra, the formula can be manipulated to find the other. 015 x 1, which equals 30. A=\$ 500+ 6\%\cdot \$ 500=\$500 \cdot (1+0. The function formula is: Where: Rate = Interest rate per period. Creating a compounding dividend investment portfolio can create a lifetime of income and by reinvesting your dividends, you'll boost your returns over time. The interest calculated on the primary principal and also on the accumulated interest of previous periods of a deposit or loan is called Compound Interest. Calculating how much interest a balance will accrue in a compounding environment uses the formula. The formula for calculating compound interest is: A = P(1 + r/n)^(nt) Where: - A is the future value of the investment or loan, including both principal and interest - P is the principal amount (initial investment or loan amount) - r is the annual interest rate (expressed as a decimal) - n is the number of times interest is compounded per year Substituting into the continuous compound interest formula: \[A=Pe^{rt}=20000e^{005\] Thus the college saving account has grown from $20,000 to $40,275. For annual compounding, multiply the initial balance by one plus your annual interest rate raised to the power of the number of time periods (years). Compound interest is a great thing when you are earning it! Compound interest is when a bank pays interest on both the principal (the original amount of money)and the interest an account has already earned To calculate compound interest use the formula below. A good example of this kind of calculation is a savings account because the future value of it tells how much will be in the account at a given point in the future. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100 (0 The total amount you would repay would be $105, the original principal plus the interest. For annual compounding, multiply the initial balance by one plus your annual interest rate raised to the power of the number of time periods (years). Nov 10, 2023 · The Compound Interest Formula. Nov 21, 2023 · The compound interest equation is used to find the accrued amount when the principal, rate, compounding period, and time are known. The Compound Interest Formula. where P is the starting principal, r is the annual interest rate, Y is the number of years invested, and n is the number of compounding periods per year. Compound interest is "interest-on-interest", or the ability of a financial instrument to generate earnings on its earnings. Compound Daily Interest is a powerful force in the world of finance. Directions: This calculator will solve for almost any variable of the continuously compound interest formula. In other words, compounding interest means reinvesting the interest rather than paying it out, so that in the following period you earn interest on the principal sum plus the previously. What Is Continuous Compound Interest? Continuous compound interest is a formula for loan interest where the balance grows continuously over time, rather than being computed at discrete intervals. Where: A is the future value of the investment/loan, including interest. Mar 15, 2024 · Simple Interest Formula. How much interest is earned on a principal of $432 invested at an interest rate of 8% compounded or one year?$34 If you borrow $101 at 7% compounded annually for seven years, how much will you pay back How to calculate interest compounded semiannually. X = P [ ( 1 + i ) n - 1 ] where P is the principal, i is the nominal interest expressed as a decimal, and n is the number of periods the interest will be compounded. We discuss compounding power, interest calculation, formula, investment, effect, and examples. If you’ve heard the term “compound interest” before, you most likely heard it in the context of certain types of loans or credit card interest. Guide to Compound Interest formula. In cell C3, type "=B3-B$2" and press enter. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: \ (\$ 100 (0 The total amount you would repay would be $105, the original principal plus the. Step 1 - We need to name cell E3 "Rate" by selecting the cell and changing the name using the "Name Box. P is the principal, which is the starting amount. Find out the formulas and examples for each method with wikiHow. Typically, interest is compounded at regular intervals, such as monthly, quarterly, or semiannually, which differs from the theoretical continuous approach. Find the balance after 3 years. Simple interest is calculated by multiplying the loan principal by the interest rate and then by the term of a loan. The compound interest formula [1] is as follows: Where: T = Total accrued, including interest. FV = P (1 + r / n) Yn. The equation for the growth of an investment with continuous compounding of interest is a first-order differential equation. 75% interest compounded quarterly. How to Calculate Compound Interest. Learn how to boost your finance career. There are two types of interest, simple and compound. What is the compound-interest formula? One very important exponential equation is the compound -interest formula, which looks like this: A=P\left (1+\cfrac {r} {n}\right)^ {nt} A= P (1+ nr)ntwhere A is the ending amount, P is the beginning amount (or "principal"), r is the interest rate (expressed as a decimal), n is the number of. A = amount of money accumulated after n years, including interest. For example, say you deposit $5,000 in a savings account that earns a 5% annual interest rate and compounds. The compound interest formula will determine A, the future value a particular investment will have Example 1: These notes are used in Lessons 25-27. Using the quarterly compound interest formula: A = P (1 + r / 4) 4 t. It does not take much to spot that this was not exactly serious research Interest is defined as the "cost of borrowing money". Mariah's estimate of the time is too low Mariah's estimate of the time is correct. 17 I'd like to know the compound interest formula for the following scenario: P = Initial Amount i = yearly interest rate A = yearly contribution or deposit added. We've created generations of people who have been encouraged to ring up debt and pay compound interest instead of collecting it. 83 earned would be due to the effect of compounding. It also calculates the other parameters of the simple interest formula. Use this simple interest calculator to find A, the Final Investment Value, using the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods. mmat news reddit Recall that m m represents the number of compounding periods that an investment remains in the account, and k k represents the number of times per year that your interest is compounded. 6. The formula for continuous compound interest is given by the equation A = P * e^ (rt), where: A is the amount of money accumulated after n years, including interest. Compounding is the simple concept of earning interest on interest, and it is one of the most fundamental ways for investors to build wealth over the long… Compounding is the simple. Advertisement Chemical compounds are substances that form wh. Interest rate variance range. Solution: Use the continuous compound interest formula, Given P = 23401 / 100) = 0 t = 3. The interest rate gets compounded yearly, and hence the formula is used to calculate the effective interest rate -. Interest is really a fee charged for borrowing the money, it is a percentage charged on the principal amount for a period of a year -- usually. Both types of investment accounts have trade-offs worth considering. 只要計算利息的周期越密，財富增長越快，而隨著年期越長. If we want to find just the compound interest then we need to subtract P from the formula. Higher returns: Reinvesting your earnings through compound interest can also yield significantly higher returns compared to simple interest. In these formulas, A is the total amount that includes both the compound interest and the principal. This gives a slightly higher final payment and follows the formula P ( 1 + r 2) 2 t = F. n is the number of times the principal is compounded in a year. golf carts for sale louisiana It uses this same formula to solve for principal, rate or time given the other known values. P = the principal amount (the initial amount invested) r = the annual interest rate. The formula for compound interest is defined as: where: S = Final Dollar Value. Calculate periodic compound interest on an investment or savings. The formula is derived from the compound interest formula by depositing \(P\) = $1 in an account and calculating how much interest it will accrue in a year (\(t\) = 1). By doing so, we can better understand the difference between simple and compound interest. In the example shown, the formula in C10 is: =FV(C6/C8,C7*C8,0,-C5) The FV function returns approximately 1647 as a final result. To calculate compound interest, do the following: Identify the principal amount (P). Understanding this concept is crucial for. How to Calculate Compound Interest. Say, you're going to run a savings scheme with one of your trusted banks. The formula for the effective interest rate is: It is called annual because of the fact that the interest is compounded annually or every year. Compound interest - meaning that the interest you earn each year is added to your principal, so that the balance doesn't merely grow, it grows at an increasing rate - is one of the most useful. Answer: The amount after 15 years = $19,287. Roughly, continuous compounding describes interest being added in the instant it is earned. Compound interest - meaning that the interest you earn each year is added to your principal, so that the balance doesn't merely grow, it grows at an increasing rate - is one of the most useful. The formula for calculating the total amount paid on a loan with compound interest is: A = P ( 1 + r n ) n t where: A = Final amount P = Initial principal balance r =. Expressed as a decimal, the interest rate is 0. Monthly Compound Interest = 5000. Interest is defined as the "cost of borrowing money". Reviewed by Chris Hindle Compound interest, or 'interest on interest', is calculated using the compound interest formula A = P*(1+r/n)^(nt), where P is the principal balance, r is the interest rate (as a decimal), n represents the number of times interest is compounded per year and t is the number of years. Whether it's youthful idealism or plain-old ambition, millennial and Gen Z workers have lofty salary expectations. How much interest is earned on a principal of $432 invested at an interest rate of 8% compounded or one year?$34 If you borrow $101 at 7% compounded annually for seven years, how much will you pay back How to calculate interest compounded semiannually. 1000 gallon stainless steel tank for sale Compound Interest Formulas Formula. Length of time, in years, that you plan to save. more. Compound Interest is calculated, after calculating the total amount over a period of time, based on the rate of interest, and the initial principal. Results presented in easy to read charts and schedule. The compound interest formula is: A = P × (1 + r/n)nt. where: A 0 : principal amount, or initial investment. The compound interest formula is: A = P × (1 + r/n)nt. Then multiply the original amount by the interest rate05 = $50 You have just calculated your annual interest! To get a monthly interest, divide this value by the number of months in a year ( 12 )17. Advertisement Compounding pharmacies don't usually get a lot of media. Solution: Use the continuous compound interest formula, Given P = 23401 / 100) = 0 t = 3. Daily compound interest formula. 6 days ago · To calculate compound interest, do the following: Identify the principal amount (P). This example assumes that $1000 is invested for 10 years at an annual interest rate of 5%, compounded monthly. The principal amount is, P = $15000. Advertisement Compounding pharmacies don't usually get a lot of media. As a wise man once said, "Money makes money Learn how to calculate compound interest in Excel using the general formula and the FV function. Learn how to boost your finance career. Are you curious about compound interest? Learn how it works in relation to investments. Test your knowledge! The formula for calculating compound interest is: A = P (1 + r/n)^ (nt) Where: A = the future value of the investment/loan, including interest. Feb 28, 2024 · Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan Mar 20, 2024 · With a compounding interest rate, it takes 17 years and 8 months to double (considering an annual compounding frequency and a 4% interest rate). The compound interest formula is: where: P is the initial principal balance; r is the interest rate (typically, this is an annual rate) n is the number of times interest compounds during each time period; t is the number of time periods; A is the ending balance, including the compounded interest In order to calculate accumulated interest, we once again must subtract out the sum of our deposits, which is still $1,620, so we now arrive at total interest of $1,78697. It excludes the effect of compounding. Feb 28, 2024 · Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan Mar 20, 2024 · With a compounding interest rate, it takes 17 years and 8 months to double (considering an annual compounding frequency and a 4% interest rate).
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The total initial amount of your loan is then subtracted from the resulting value. Test your knowledge! The formula for calculating compound interest is: A = P (1 + r/n)^ (nt) Where: A = the future value of the investment/loan, including interest. Therefore the solution to this initial value. 1. The total initial amount of your loan is then subtracted from the resulting value. To calculate this: Use the compound interest formula: FV = P × (1 + (r / m))(m × t) Substitute the values. The first equation is for the future value under simple interest method and the second one is for future value under compound interest method. The Excel formula would be F = -FV (0 The table below shows how the calculations work each compound period. For example, say you deposit $5,000 in a savings account that earns a 5% annual interest rate and compounds. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: \ (\$ 100 (0 The total amount you would repay would be $105, the original principal plus the. What is Continuously Compounded Interest? Continuously compounding interest is the interest earned on both the initial principal invested and the accumulated interest from previous periods. 04, so the formula would be: Interest = $10,000 * 0. The formula for compound interest is P (1 + r/n)^ (nt), where P is the initial principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods ( 5 votes) The Four Formulas. Roth IRAs and 529 savings plans are great for saving for college—both are taxed upfront, allowing you to withdr. In other words, compounding interest means reinvesting the interest rather than paying it out, so that in the following period you earn interest on the principal sum plus the previously. patriot tractor somersworth nh It does not take much to spot that this was not exactly serious research Interest is defined as the "cost of borrowing money". It also shows how to calculate compound interest with daily, monthly, and yearly rates. Quartz is a guide to the new global economy for people in business who are excited by change. The formula for compounded interest is based on the principal, P, the nominal interest rate, i, and the number of compounding periods. After using this formula, the simple interest earned would be $120. Advertisement Compounding pharmacies don't usually get a lot of media. First of all, take the interest rate and divide it by one hundred05. Interest, in its most simple form, is calculated as a percent of the principal. Monthly Contribution. Let us discuss the formula for compound interest. 02 / 365 ) 365 × 30 = $182,208 Over the 30-year period, compound. Which of the following most closely approximates the total amount in the account after that period of time? Continuous Compounding. Suppose we have the following information to calculate compound interest in a table excel format (systematically). roger ruch Use this simple interest calculator to find A, the Final Investment Value, using the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods. If the account was compounded daily, the amount earned would be higher. Use the continuous compound interest calculator to learn the final balance of your investment or savings with interest compounded continuously. Compounding is the process where the value of an investment increases because the earnings on an investment, both capital gains and interest, earn interest as time passes. The basic formula for Compound Interest is: FV = PV (1+r) n. Here we discuss compound interests using their formula, graph, calculations, & examples. The table starts with an initial principal of P 0 =4000. The initial investment, interest rate, duration and the formula are exactly the same as in the above example, only the compounding period is different: PV = $2,000 Below is the compound interest with contributions formula: P = (PMT [ ( (1 + r) n - 1) / r]) (1 + r) Where: P = The future value of the savings you expect to be paid in the future. Pop up mortgage calculator. The image of financial services has always been dominated by the frenetic energy of the trading floor, where people dart and weave en masse. How to Calculate Compound Interest. The formula for continuous compound interest is given by the equation A = P * e^ (rt), where: A is the amount of money accumulated after n years, including interest. Consider the example described below. Thousands of practice questions and explanation videos at:http://wwwcom The difference between simple interest and compound interest is that simple interest builds only on the principal amount, while compound interest builds on both the principal and p. Approximately how much interest is earned on the investment? a67 b72 c37 d37, Certain investments compound interest at different intervals. chaps khaki shorts r = Annual Interest Rate. For annual compounding, multiply the initial balance by one plus your annual interest rate raised to the power of the number of time periods (years). In this video, we expand the equation to calculate simple interest for a single period, P* (1+r), to calculate interest when interest is charged for more than one period and that interest is compounded at different intervals. 2) which will return a balance of $1221. The variables are: P - the principal (the amount of money you start with); r - the annual nominal interest rate before compounding; t - time, in years; and n - the number of compounding periods in each. n = number of times compounded per year. t = number of years. To examine several investments to see which has the best rate, we find and compare the effective rate. Step 2: Contribute. From the Compound Interest formula (shown above) we can compound "n" periods using But the interest rate won't be "r", because it has to be chopped into "n" periods like this: r / n. Which of the following most closely approximates the total amount in the account after that period of time? Continuous Compounding. 75% interest compounded quarterly. The interest is compounded \(4 \times 12 = 48\) times. Here are the steps to solving the compound interest formula: 11 An application of exponential functions is compound interest. What effect does the size of the compounding interval have on. The interest calculated on the primary principal and also on the accumulated interest of previous periods of a deposit or loan is called Compound Interest. This is the number of times you amount gets compounded. It factors in your regular contributions, compounding freque. Find out the formulas and examples for each method with wikiHow.
For monthly compounding, the periodic interest rate is simply the annual rate divided by 12, because there are 12 months or “periods” during the year. The following exercises explore what happens when a person deposits money in an account earning compound interest Find the present value of $500,000 in an account that earns 3. The number of compounding periods is equal to the term in years multiplied by the corresponding factor. The formula for calculating the total amount paid on a loan with compound interest is: A = P ( 1 + r n ) n t where: A = Final amount P = Initial principal balance r =. After using this formula, the simple interest earned would be $120. Review sample compound interest problems to be ready for your exam. In much simpler terms, Compound interest is the "interest on interest". Simple interest, or "non-compounding interest", is a type of interest rate pricing wherein the amount of interest owed is determined only by the principal of the debt obligation, such as a loan. humane society of southern arizona thrift store photos The first compound telescope was made b. Regardless of your rate, the more often interest is pa. It is exactly what the compound interest does to the money. Thousands of practice questions and explanation videos at:http://wwwcom The difference between simple interest and compound interest is that simple interest builds only on the principal amount, while compound interest builds on both the principal and p. Quarterly Compounding: 4x Per Year. Compound interest multiplies savings or debt at an accelerated rate Compound interest is taken from the initial - or principal - amount on a loan or a deposit, plus any interest that has already accrued. A = Final balance (including initial amount plus all accumulated interest) P = Principal or initial investment The formula for calculating daily compound interest is as follows: Daily Compound Interest = Ending Investment - Start Amount. Scientists at the University of Cape Town’s Drug Discovery and Development Centre (H3D) say they have found. electrical contractor near me 4000 into an account paying 6% annual interest compounded. Soma Compound With Codeine (Oral) received an overall rating of 10 out of 10 stars from 2 reviews. The compounding frequency each year is 12. The compounding frequency each year is 12. unique door wreaths The formula for the effective interest rate is: It is called annual because of the fact that the interest is compounded annually or every year. 02 / 1 ) 1 × 30 = $181,136 For daily compounding: $100,000 × ( 1 + (. The traditional hiring process puts job seekers at a disadvantage. Test your knowledge! The formula for calculating compound interest is: A = P (1 + r/n)^ (nt) Where: A = the future value of the investment/loan, including interest. Roth IRAs and 529 savings plans are great for saving for college—both are taxed upfront, allowing you to withdr. This reinvestment of interest is called compounding.
Typically, interest is compounded at regular intervals, such as monthly, quarterly, or semiannually, which differs from the theoretical continuous approach. 1, it would be 100% plus 7%, or 1 Let's go to 3 years. Compounding occurs when the money earned from investments is reinvested for the chance to gain even more. Compounding interest requires more than one period, so let's go back to the example of Derek borrowing $100 from the bank for two years at a 10% interest rate. The formula to calculate compound interest is: A = P (1 + \frac {r} {n})^ {nt} A = P (1+ nr)nt. The function formula is: Where: Rate = Interest rate per period. Using the same calculation methods, we could compound every hour, every minute, and even every second. Creating a compounding dividend investment portfolio can create a lifetime of income and by reinvesting your dividends, you'll boost your returns over time. To compute compound interest we need to know. After using this formula, the simple interest earned would be $120. Applying the Compound-Interest Formula. 6 days ago · To calculate compound interest, do the following: Identify the principal amount (P). You want to know what your total amount after a certain period (years) will be. Compounded annual growth rate, i, CAGR, is used mostly for financial applications where single growth for a period needs to be calculated. For annual compounding: $100,000 × ( 1 + (. However, we'll break it down so you have a good understanding of how the calculator works. Instead of compounding interest on an monthly, quarterly, or annual basis, continuous compounding will effectively reinvest gains perpetually. PMT = The amount of each contribution. Interest is paid either annually. The initial amount P is also called the principal. r is the interest rate. Nov 21, 2023 · The compound interest equation is used to find the accrued amount when the principal, rate, compounding period, and time are known. 28, in the bank for another year, the final amount will be $23328(28(1 + 94. catholic charities appointment Example A (repeated from Lecture 4. To examine several investments to see which has the best rate, we find and compare the effective rate. Step 2: Contribute. example 4: Determine the present value of $1000 at a 12% annual interest rate compounded quarterly at the end of two years. For annual compounding: $100,000 × ( 1 + (. P = initial principal (e your deposit, initial balance, “current amount saved”) r = interest rate offered by the savings account. r is the annual interest rate (as a decimal). In compound interest the interest amount is added back to the principle. To calculate compound interest, do the following: Identify the principal amount (P). as, we know that Compound interest is an interest accumulated on the principal and interest together over a given time period. If \(N\) is the number of years, then \(m = N k\). 07 to the 3rd power, or 1. The interest is compounded \(4 \times 12 = 48\) times. Compound interest is when the interest you earn on a balance in a savings or investing account is reinvested, earning you more interest. The initial investment, interest rate, duration and the formula are exactly the same as in the above example, only the compounding period is different: PV = $2,000 Below is the compound interest with contributions formula: P = (PMT [ ( (1 + r) n - 1) / r]) (1 + r) Where: P = The future value of the savings you expect to be paid in the future. Compound interest is calculated using the compound interest formula: A = P (1+r/n)^nt. Learn how to use compound interest formula in Excel. horse hitching post How To Calculate Daily Compound Interest in Excel. The basic formula for compound interest is as follows: A t = A 0 (1 + r) n. The following examples use the compound interest formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) Example \(\PageIndex{1}\) If $3500 is invested at 9% compounded monthly, what will the future value be in four years? Solution. example 4: Determine the present value of $1000 at a 12% annual interest rate compounded quarterly at the end of two years. The formula is derived from the compound interest formula by depositing \(P\) = $1 in an account and calculating how much interest it will accrue in a year (\(t\) = 1). Our next objective is to derive a formula to model continuous compounding. FV = PVe^it = $1,000 * 212*5 = $1,822 Given this, the interest earned would be $1000 times 1 year times 12%. The formula for compound interest is: COMPOUND INTEREST FORMULA. Calculating how much interest a balance will accrue in a compounding environment uses the formula. Size: Calculate A = P(1 + r n)(n⋅t) A = P ( 1 + r n) ( n ⋅ t) After 4 years , your original $9, compounded 3 times per year, will become a final amount of $9 Worksheet #1 on Continuously Compounded Interest (no logs) Worksheet #2 (requires use of logs) Compound Interest Formula. The continuous compound interest formula is a mathematical tool used in finance and economics. Creating a compounding dividend investment portfolio can create a lifetime of income and by reinvesting your dividends, you'll boost your returns over time. If \(N\) is the number of years, then \(m = N k\). For annual compounding, multiply the initial balance by one plus your annual interest rate raised to the power of the number of time periods (years). Demonstration of Various Compounding The following table shows the final principal (P), after t = 1 year, of an account initially with C = $10000, at 6% interest rate, with the given compounding (n). Frequently Asked Questions. Roth IRAs and 529 savings plans are great for saving for college—both are taxed upfront, allowing you to withdr. The compound interest formula solves for the future value of your investment ( A ). The formula for the Compound Interest is, The differential equation above can be easily solved as a separable differential equation. Calculate the effective interest rate for continuously compounding interest. Scientists at the University of Cape Town’s Drug Discovery and Development Centre (H3D) say they have found. P0 P 0 is the starting balance of the account (also called an initial deposit, or principal) r r is the annual interest rate in decimal form.