The amount after n years An is equal to the initial amount A0 times one plus the annual interest rate r divided by the number of compounding periods in a year m raised to the power of m times n:
An is the amount after n years (future value).
A0 is the initial amount (present value).
r is the nominal annual interest rate.
m is the number of compounding periods in one year.
n is the number of years.
Calculate the future value after 10 years present value of $5,000 with annual interest of 4%.
A0 = $5,000
r = 4% = 4/100 = 0.04
m = 1
n = 10
A10 = $5,000·(1+0.04/1)(1·10) = $7,401.22
Calculate the future value after 8 years present value of $35,000 with annual interest of 3% compounded monthly.
A0 = $35,000
r = 3% = 3/100 = 0.03
m = 12
n = 8
A8 = $35,000·(1+0.03/12)(12·8) = $44,480.40