Question

Jacob's friend, Albert, borrows today with a promise to repay $13,705 in 16 years. If Jacob could earn 6 percent annually on the any investment he makes today, how much would he be willing to lend Albert today? Hint: How much can Jacob lend Albert today (PV?) so that he can achieve his expected 6\% return (I/Y) when Albert pays back the $13,705 (FV) 16 years from now (N)? Round to nearest two decimals if needed. Do not type the $ symbol.

Answer 1

To find out how much Jacob should lend Albert today to get a 6% return over 16 years, we use the present value formula. The calculation based on the provided details is: PV = 13705 / (1 + 0.06)^16, which will yield the amount Jacob should lend.

Step-by-step explanation:

Jacob's friend Albert borrows money with a promise to repay a sum after a certain number of years, and Jacob is assessing how much he should lend based on an expected return from his investment. To calculate the present value (PV) of the amount that Albert will repay in the future, we can use the formula for the present value of a single future amount, which is: PV = FV / (1 + r)^n. Here, FV is the future value which is $13,705, r is the annual interest rate which is 6% or 0.06, and n is the number of years which is 16.

Plugging these values into the formula gives us: PV = 13705 / (1 + 0.06)^16. Computing this will provide the amount that Jacob would be willing to lend Albert today so that he can achieve his expected 6% return when Albert repays him in 16 years.