An investment of $30 325 is accumulated at 9.45% compounded quarterly for nine and one-half years. At that time the interest rate is changed to 9.45% compounded monthly. How much is the investment worth two years after the change in interest rate?
A) $73646.89
B) $88902.62
C) $49319.03
D) $89520.33
E) $88773.12

Question

Quizplus · Accepted Answer

First, calculate the amount after the initial 9.5 years with quarterly compounding using the formula A = P(1 + r/n)^(nt), where P = $30,325, r = 9.45% or 0.0945, n = 4 (quarterly), and t = 9.5 years. This gives A1 = $30,325(1 + 0.0945/4)^(4*9.5). After 9.5 years, switch to monthly compounding for 2 more years with the new principal being the amount from the first period, A1, r = 0.0945, n = 12 (monthly), and t = 2 years. Calculate A2 = A1(1 + 0.0945/12)^(12*2). The final amount is approximately $88,902.62.

An Investment of $30 325 Is Accumulated at 9