Question

Your brother has asked you for a loan and has promised to pay you $7,100 at the end of three years. If you normally invest to earn 8.20 percent per year, how much will you be willing to lend to your brother if you view this purely as a financial transaction (i.e., you don’t give your brother a special deal)? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.)

Answer 1

5605.01 dollars

Explanation:

Given that after 3 years your brother will pay your 7100 dollars.

If invested otherwise, interest is 8.20 percent per year

Let P be the amount invested

Then after 3 years at compound interest final amount

A =
`P(1+(8.2)/(100))^3\\ =P(1.082)^3`

This must be less than or equal to 7100 if willing to lend to brother

i.e.
`P(1.082)^3 \leq 7100\\P\leq 5605.01`

So willing to lend upto 5605.01 dollars