Question

Compute the requested value(s) for each scenario. Show all component numbers that factor into determination of the final answer(s) a. Your brother in-law is offering to pay you $40,000 ten years from now in exchange for a $15,000 investment today. If you accept his offer, what annual rate of interest would you earn on your investment?

Answer 1

The annual rate of interest for the offer of receiving $40,000 ten years from now in exchange for a $15,000 investment today is approximately 8.384%.

Step-by-step explanation:

To find the annual rate of interest your brother-in-law's offer represents, we can use the future value formula for compound interest. The formula is Future Value = Present Value x (1 + Interest Rate)Number of Years. Plugging the values in, $40,000 is the future value, $15,000 is the present value, and the number of years (t) is 10.

We need to solve for the interest rate (r), so we have:
$40,000 = $15,000 x (1 + r)10

Dividing both sides by $15,000 we get:
(40,000 / 15,000) = (1 + r)10

2.66667 = (1 + r)10

Taking the 10th root of both sides, we find:
1 + r = 1.08384 (approximately)

Therefore, r = 0.08384 or 8.384%.

The annual rate of interest you would earn on your investment if you accept your brother-in-law's offer is approximately 8.384%.