Question

If an investment of $40,000 is earning an interest rate of 12.00%, compounded annually, then it will take for this investment to reach a value of $56,197.12—assuming that no additional deposits or withdrawals are made during this time. Which of the following statements is true—assuming that no additional deposits or withdrawals are made? If you invest $5 today at 15% annual compound interest for 82.3753 years, you’ll end up with $100,000. If you invest $1 today at 15% annual compound interest for 82.3753 years, you’ll end up with $100,000.

Answer 1

1) we can use the future value formula to solve this:

future value = present value x (1 + r)ⁿ

$56,197.12 = $40,000 x (1 + 12%)ⁿ

1.12ⁿ = $56,197.12 / $40,000 = 1.404928

n = log 1.404928 / log 1.12 = 3 years

2) Which of the following statements is true - assuming that no additional deposits or withdrawals are made?

• If you invest $1 today at 15% annual compound interest for 82.3753 years, you’ll end up with $100,000.

FV = $1 x 1.15⁸²°³⁷⁵³ = $100,000.65 ✓