Question

Manny invests $100 in an account that is compounded continuously at an annual interest rate of 2%, according to the formula
A
=
P
e
r
t
, where
A
is the amount accrued,
P
is the principal, r is the rate of interest, and t is the time, in years. In 20 years, how much will Manny’s investment be worth to the nearest dollar?

Answer 1

A = Pe^{rt} = 100 e^{0.02·20} = 100 e^{0.4} ≈ 100(1.4918247) ≈ $149 (to the nearest dollar).