You borrow $2500 today.The loan is due in 5-years,with interest at j₂ = 8%.It is agreed that you can instead pay $X two years from now and $1500 three years from now.If money is worth j₁₂ = 6%,what is the value of X?

Question

Quizplus · Accepted Answer

Using the concept of present value, we find that the present value of the loan is:
PV = $2500/(1+0.08)^5 = $1724.99
Now, we need to find the present value of the two payments that will be made in the future. Using the same concept, we get:
PV of X = $X/(1+0.06)^2
PV of $1500 = $1500/(1+0.06)^3
Since the loan will be paid off after the two future payments, the present value of these payments should equal the present value of the loan:
PV of X + PV of $1500 = PV of loan
Substituting the values, we get:
$X/(1+0.06)^2 + $1500/(1+0.06)^3 = $1724.99
Solving for X, we get:
X = $1679.54
Therefore, the best choice is (A).

You Borrow $2500 Today