A university student wins a scholarship worth $50,000.Instead of the lump sum,she chooses to be paid by 48 monthly payments of $R,with the first monthly payment to be made 5 months from now.If the money earns interest at j₁₂ = 9%,what is the monthly payment? A)$1291.62 B)$1282.00 C)$1272.46 D)$1244.25

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the scholarship, which is:
PV = $50,000 / (1 + 0.09/12)^5 = $38,658.51

Then, we can use the formula for the monthly payment of an annuity:
R = PV / ( (1 - (1+i)^(-n)) / i ), where i = 0.09/12 and n = 48

Substituting the values, we get:
R = $38,658.51 / ( (1 - (1+0.09/12)^(-48)) / (0.09/12) ) ≈ $1282.00

Therefore, the best choice is B, with a monthly payment of $1282.00.

A University Student Wins a Scholarship Worth $50,000