A loan of $5000 is taken out today.It is due with interest at j₄ = 8% in 2 years.Instead,the borrower negotiates with the lender to pay $2500 in 1 year and $X in 3 years.If the lender can reinvest any payment at j₂ = 5%,what is the value of X?

Question

Quizplus · Accepted Answer

First, we need to find the amount the borrower would need to pay back in 2 years with the 8% interest:

$5000 * (1 + 0.08)^2 = $5832

Next, we need to find the present value of the two new payments, discounted back to today:

PV($2500, 1 year) = $2500 / (1 + 0.05) = $2380.95

PV($X, 3 years) = $X / (1 + 0.05)^3

Since the loan is being renegotiated, the sum of these two present values should equal the original loan amount of $5000:

$2380.95 + ($X / (1 + 0.05)^3) = $5000

Solving for X, we get:

$X = $3395.34

Therefore, the best choice is C.

A Loan of $5000 Is Taken Out Today