Twenty years ago Freddie invested $2,000. For the first 10 years he earned 13% compounded semi-annually. For the next 10 years he earned 8% compounded quarterly. What was the value of the investment now, at the end of the 20 years?
A) $5,927
B) $9,185
C) $17,292
D) $14,732
E) $15,561

Question

Quizplus · Accepted Answer

First, calculate the value after the first 10 years with 13% semi-annual compounding: $ A = 2000 \times (1 + \frac{0.13}{2})^{20} $. Then, use this amount as the principal for the next 10 years with 8% quarterly compounding: $ A = A \times (1 + \frac{0.08}{4})^{40} $. The final amount is approximately $15,561.

Twenty Years Ago Freddie Invested $2,000