Interest Rate Problem

Question

Nancy wants to invest $4000 in saving certificates that bear an interest rate of 8.75% per year, compounded semiannually. How long a time period should she choose to save an amount of $5000? (Round your answer to two decimal places.)

Answer 1

5000 = 4000(1 + 0.0875/2)^2t

5/4 = (1 + 0.0875/2)^2t

log(5/4) = 2tlog(1 + 0.0875/2)

t = log(5/4)/2log(1 + 0.875/2)

t = 2.61 years