Question

5. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $9,200 will be worth $15,767.18 seven years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made? 8.00% 6.40% 5.83% 0.24% If an investment of $50,000 is earning an interest rate of 8.00%, compounded annually, then it will take for this investment to reach a value of $89,052.92—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

answer to first question:

(1 + i)⁷ = $15,767.18 / $9,200 = 1.713824

⁷√(1 + i)⁷ = ⁷√1.713824

1 + i = 1.08

i = 8%

answer to second question:

(1 + 8%)ⁿ = $89,052.92 / $50,000 = 1.7810584

1.08ⁿ = 1.7810584

n = log 1.7810584 / log 1.08 = 0.25067816 / 0.033423755 = 7.5 years

answer to third question:

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