Question

Kreskin deposits $8,039 every six months, increasing the amount deposited by 2.5% with each subsequent deposit. The account pays a nominal annual interest rate of 5%, compounded biannually (twice a year). How much will Kreskin have in the account at the end of 21 years?

Answer 1

g = 2.5%

I = 5% compounded biannually (twice a year) = 5% / 2 = 2.5% per semiannual period

n = 21 yrs = 21 * 2 = 42 semi annual periods

Present value of geometric series when I is equal to g is C*N/ (1+i)

P = 8039 * 42 / (1+0.025) = 329402.93

Future worth of account = 329402.93 *(1+0.025)^42 = 329402.93 *(1.025)^42 = 929244.07 ~ 929244 (Nearest Dollar)