A loan is to be paid by installments of $800 1-month from now,$600 3-months from now,and $500 4-months from now.Instead of this payment scheme,the borrower wishes to make one single payment 2 months from now.What is the amount of the alternative single payment using a focal date of 3 months and r = 6%?
A)$1905.51
B)$1901.00
C)$1896.03
D)$1890.55

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the original payment scheme using a focal date of 3 months and r=6%:

PV = 800/(1+0.06)^1 + 600/(1+0.06)^3 + 500/(1+0.06)^4
PV = $1771.30

Next, we need to find the single payment that would be equivalent to the original payment scheme using a focal date of 3 months and r=6%. We can use the formula for the present value of an annuity to solve for the single payment:

PV = P/ (1+r)^t
P = PV*(1+r)^t
P = $1771.30*(1+0.06)^3
P = $1896.03

Therefore, the alternative single payment that would be equivalent to the original payment scheme is $1896.03.

A Loan Is to Be Paid by Installments of $800