Compound Interest

This page contains the compound interest formulas, a compound interest calculator and information on how to perform compound interest calculations using Excel. Compound Interest Calculator * Present Value:  Future Value: Number of Periods: Interest  Rate(%): Insert the 3 variables you know. Press Calculate in the row of the variable you wish to calculate. Click here for an example of how to use the calculator. Click here for an example where the interest rate is compounded more than once a year   Equations for Compound Interest These are the equations for compound interest: pv = fv / (1 + i) n n = log ( fv / pv ) / log (1 + i) fv = pv * (1 + i) n i = ( fv / pv ) ( 1 / n ) - 1 where pv = present value fv = future value n = number of periods i = interest rate Click here for an example of how to use the formulas If the interest is compounded more than once a year then the formula for fv becomes: fv = pv * (1 + i/t) nt where t = number of times interest is compounded a year If the interest is compounded continuously it becomes fv = pv * e ni where e is approximately 2.71828 Excel Excel does not provide functions for compound interest so you have to create your own. Below is an example of how to do this.   Simply click inside the window below, use your cursor to highlight the script, and copy (type Control-c ) the script. Start Microsoft Excel. Start the Visual Basic Editor. (ALT+F11) On the Insert menu, click Module. Press Ctrl+V      Function PV_yabz(fv, N, i) As Double pv_yabz = fv / ((1 + i) ^ N) End Function Function FV_yabz(pv, N, i) As Double fv_yabz = pv * (1 + i) ^ N End Function Function I_yabz(pv, fv, N) As Double i_yabz = (fv / pv) ^ (1 / N) - 1 End Function Function N_yabz(pv, fv, i) As Double N_yabz = Log(fv / pv) / Log(1 + i) End Function This creates the following functions: PV_yabz(fv, N, i) Note:  interest rate is input as a real number, not as a percentage. For example 8% would be input as .08 FV_yabz(pv, N, i) I_yabz(pv, fv, N) N_yabz(pv, fv, i)      You can also do compound interest calculations using the Excel functions: RATE(nper,pmt,pv,fv,type,guess) FV(rate,nper,pmt,pv,type) PV(rate,nper,pmt,fv,type) NPER(rate,pmt,pv,fv,type) The Excel functions are useful when you want to calculate compound interest when making regular payments as in a mortgage or annuity. They are powerful but slightly complex to use. Click here to see an Excel Compound Interest Calculator, together with a worked example of paying off a debt. (Press cancel if asked for authentication) Calculating Compound Interest in your Head In you are a financial advisor or financial professional you can impress clients by performing compound interest calculations in your head. The trick is to us the Rule of 72. Divide 72 by the interest rate to see how long it takes to double. For example, $1 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $2. This holds pretty much true for all percentages under 20%. *please note that the compound interest calculator may not work under some versions of Netscape and Opera.