Avangard is an art school that borrows money to expand its studio. The loan agre

Question

Avangard is an art school that borrows money to expand its studio. The loan agreement requires paying a fixed payment (F) of $2,400 at the end of each year for the next five years, with an annual interest rate (i) of 9%. Avangard calculates the present value of the loan (PV) using the following formula: I x{1-[1/(1+ i)]}/F F x {1 - [1/(1 + i)]^5}/i F x {1 - [1/(1 + i)]^5}/(i + 1) Avangard's present value of the loan is. Suppose that the loan agreement requires Avangard to make monthly fixed payments of $200 for the next five years, while the annual interest rate stays at 9%. Avangard calculates the present value of the loan at using the following formula: {1-[1/(1 + Interest Rate per month)]60}/Interest Rate per month Interest Rate per month x{1-[1/(1 + Fixed Payment)]^60}/Fixed Payment Fx {1 - [1/(1 + Interest Rate per month)]^60}/Interest Rate per month

Explanation / Answer

PV of loan = F x PVIFA(r%, N) where

PVIFA = [1 - (1 / (1 + i)N)] / i

(1) N = 5, i = 9%

PV = F x [1 - (1 / (1 + i)5)] / i

= $2,400 x [1 - (1 / (1.09)5)] / 0.09 = $2,400 x 3.8897 = $9,335.28

(2) 3rd option is correct.

PV = F x [1 - (1 / (1 + i)60)] / i where

i: Interest rate per month

60: Number of months = 5 x 12

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