You owe $4510 due in 7 months. In addition you owe $3780 due in 13 months and $5125 due in 21 months. You are paying 8.64% compounded monthly on your loan. What single amount three months from now will pay off the entire loan of the three future payments?
A) $12 440.86
B) $12 040.86
C) $12 404.86
D) $12 444.86
E) $12 884.86

Question

Quizplus · Accepted Answer

We need to find the present value of the future payments, which will be due in 4, 10, and 18 months respectively. To find the present value, we need to discount the future payments back to the present time (3 months from now). We can use the formula for present value of an annuity:

PV = C*[1 - (1+r)^(-n)]/r

where PV is the present value, C is the future payment, r is the monthly interest rate, and n is the number of months until the payment is due.

For the first payment of $4510 due in 7 months, we have:

PV1 = 4510*[1 - (1+0.0864/12)^(-4)]/(0.0864/12) = 4061.24

For the second payment of $3780 due in 13 months, we have:

PV2 = 3780*[1 - (1+0.0864/12)^(-10)]/(0.0864/12) = 3294.81

For the third payment of $5125 due in 21 months, we have:

PV3 = 5125*[1 - (1+0.0864/12)^(-18)]/(0.0864/12) = 4061.81

The total present value of the future payments is:

PV = PV1 + PV2 + PV3 = 11417.86

Now, we need to find the single amount that will pay off this present value in 10 months (3 months from now + 7 months for the first payment + 13 months for the second payment + 21 months for the third payment). We can use the formula for future value of a present value:

FV = PV*(1+r)^n

where FV is the future value, PV is the present value, r is the monthly interest rate, and n is the number of months until the payment is due.

We have:

FV = 11417.86*(1+0.0864/12)^10 = 12404.86

Therefore, a single payment of $12,404.86 made 3 months from now will pay off the entire loan. The best choice is C.

You Owe $4510 Due in 7 Months