Which formula gives the future value after n years with annual compounding at rate r?

• A. FV = PV(1 + r)^n
• B. FV = PV e^(rn)
• C. FV = PV (1 + r t)
• D. FV = PV / (1 + r)^n

Answer: (A)

The key idea is that with annual compounding, interest is added once per year and the growth happens in discrete steps. Each year the amount grows by a factor of (1 + r). After n years, you multiply n such factors, giving FV = PV × (1 + r)ⁿ. This captures how the account compounds year after year, so the future value increases not just linearly but exponentially with the number of years.

For example, with r = 0.05 and PV = 100, after 3 years you’d have 100 × (1.05)³ ≈ 115.76, illustrating the effect of compounding.

Other forms aren’t appropriate here: continuous compounding uses e^(rn) instead of (1 + r)ⁿ; simple interest uses PV × (1 + r t) with no growth from interest on interest; and the expression PV / (1 + r)ⁿ would represent discounting or a wrong orientation for future value.