Compounding and Your Return CalculatorHow interest is calculated can greatly affect your savings. The more often interest is compounded, or added to your account, the more you earn. This calculator demonstrates how compounding can affect your savings, and how interest on your interest really adds up! Show
Information and interactive calculators are made available to you as self-help tools for your independent use and are not intended to provide investment advice. We cannot and do not guarantee their applicability or accuracy in regards to your individual circumstances. All examples are hypothetical and are for illustrative purposes. We encourage you to seek personalized advice from qualified professionals regarding all personal finance issues. Calculator UseCalculate the future value return for a present value lump sum investment, or a one time investment, based on a constant interest rate per period and compounding. To include an annuity use a comprehensive future value calculation. Periodcommonly a period will be a year but it can be any time interval you want as long as all inputs are consistent.Investment (PV)is the present value or principal amount to be invested.Interest Rate (R)is the annual nominal interest rate or "stated rate" in percent. r = R/100, the interest rate in decimalNumber of Periods (t)commonly this will be number of years but periods can be any time unit. Enter whole numbers or use decimals for partial periods such as months for example, 7.5 years is 7 yr 6 mo.Compounding (m)is the number of times compounding occurs per period. If a period is a year then annually=1, quarterly=4, monthly=12, daily = 365, etc.Continuous Compoundingis when the frequency of compounding (m) is increased up to infinity. Enter c, C or Continuous for m.Interest Rate (i)i = (r/m); interest rate per compounding period.Total Number of Periods (n)n = mt; is the total number of compounding periods for the life of the investment.Future Value (FV)the calculated future value of our investmentFVIFFuture Value Interest Factor that accounts for your input Number of Periods, Interest Rate and Compounding Frequency and can now be applied to other present value amounts to find the future value under the same conditions.Future Value Formula for a Present Value:\( FV = PV\left(1+\frac{r}{m}\right)^{mt} \) where r=R/100 and is generally applied with r as the yearly interest rate, t the number of years and m the number of compounding intervals per year. Although, we can think of r as a rate per period, t the number of periods and m the compounding intervals per period where a period is any interval of time. We can reduce this to the more general \( FV = PV(1+i)^n \) where i=r/m and n=mt with i the rate per compounding period and n the number of compounding periods. When m approaches infinity, m → ∞ (continuous compounding) \( FV = PVe^{rt} \) Future Value Formula Derivations Example Future Value Calculations for a Lump Sum Investment: You put $10,000 into an ivestment account earning 6.25% per year compounded monthly. You want to know the value of your investment in 2 years or, the future value of your account.
\( FV = \$10,000(1+\frac{0.0625}{12})^{12\times2}= \$11,327.81 \)
Share this Answer Link: help Calculator UseCalculate the present value investment for a future value lump sum return, based on a constant interest rate per period and compounding. This is a special instance of a present value calculation where payments = 0. The present value is the total amount that a future amount of money is worth right now. Periodcommonly a period will be a year but it can be any time interval you want as long as all inputs are consistent.Future Value (FV)is the future value sum of your investment that you want to find a present value forNumber of Periods (t)commonly this will be number of years but periods can be any time unit. Enter whole numbers or use decimals for partial periods such as months for example, 7.5 years is 7 yr 6 mo.Interest Rate (R)is the annual nominal interest rate or "stated rate" in percent. r = R/100, the interest rate in decimalCompounding (m)is the number of times compounding occurs per period. If a period is a year then annually=1, quarterly=4, monthly=12, daily = 365, etc.Continuous Compoundingis when the frequency of compounding (m) is increased up to infinity. Enter c, C or Continuous for m.Rate (i)i = (r/m); interest rate per compounding period.Total Number of Periods (n)n = mt; is the total number of compounding periods for the life of the investment.Present Value (PV)the calculated present value of your future value amountPVIFPresent Value Interest Factor that accounts for your input Number of Periods, Interest Rate and Compounding Frequency and can now be applied to other future value amounts to find the present value under the same conditions.PeriodTime period. Typcially a period will be a year but it can be any time interval as long as all inputs are in the same time unit.Future Value (FV)Future value of a lump sum.Number of Periods (t)Number of years or time periods.PerpetuityFor a perpetual annuity t approaches infinity. For "Number of Periods (t)" enter p or perpetuity. Interest Rate (R)The annual nominal interest rate or stated rate per period, as a percentage.Compounding (m)The number of times compounding occurs per period. If a period is a year enter:• 1 for annual compounding • 4 for quarterly compounding • 12 for monthly compounding • 365 for daily compounding Continuous CompoundingFor frequency of compounding (m) approaches infinity. For "Compounding (m)" enter c or continuous. Payment Amount (PMT)The amount of the cash flow annuity payment each period.Growth Rate (G)If this is a growing annuity, enter the growth rate per period of payments in percentage form.Payments per Period (Payment Frequency, q)How often payments are made each period. If a period is a year enter: • 1 for annual payments • 4 for quarterly payments • 12 for monthly payments • 365 for daily payments Payments at Period (Type)Specify whether payments occur at the end of each payment period (ordinary annuity, in arrears) or if payments occur at the beginning of each payment period (annuity due, in advance)Present Value (PV)The present value of any future value lump sum plus future cash flows (payments) Present Value Formula for a Future Value:\( PV = \dfrac{FV}{(1+\frac{r}{m})^{mt}} \) where r=R/100 and is generally applied with r as the yearly interest rate, t the number of years and m the number of compounding intervals per year. We can reduce this to the more general \( PV = \dfrac{FV}{(1+i)^n} \) where i=r/m and n=mt with i the rate per compounding period and n the number of compounding periods. When m approaches infinity, m → ∞ (continuous compounding) \( PV = \dfrac{FV}{e^{rt}} \) See the present value calculator for derivations of present value formulas. Example Present Value Calculations for a Lump Sum Investment: You want an investment to have a value of $10,000 in 2 years. The account will earn 6.25% per year compounded monthly. You want to know the value of your investment now to acheive this or, the present value of your investment account.
\( PV = \dfrac{\$10,000}{(1+\frac{0.0625}{12})^{12\times2}}= \$8,827.83 \) Follow CalculatorSoup:  What's the present value when interest rates are 7.5 percent of a $200 payment made every year forever Round your answer to 2 decimal places?Answer: The present value of $170 paid every year is $2,266.67.
What is the present value of a 3 year annuity of $100 if the discount rate is 6 %? Do not round intermediate calculations Round your answer to 2 decimal places?Applying the formula, the present value of the annuity is: 100(1−(1+6%)−3)6%=267.30.
What is the present value of an annuity that pays $150 per year for 10 years if the interest rate is 8%?Answer and Explanation: The calculated present value of the annuity is $12,309.97.
Which of the following will increase the present value of an annuity?The present value increases with number of payments, amount of payments, and decreases with the discount rate.
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Whats the interest rate of a 7 year annual $3800 annuity with present value of $20000?
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