Question

You are borrowing $26,750 to buy a car. The terms of the loan call for monthly payments for five years at 6.50 percent interest. What is the amount of each payment?

A.	$498.17
B.	$504.97
C.	$523.39
D.	$533.93
E.	$566.84

Answer 1

You are borrowing $26,750 to buy a car. The terms of the loan call for monthly payments for five years at 6.50 percent interest. What is the amount of each payment?

We can solve this using present value of annuity formula,

Because here the borrowing amount of $26750 is the present value of monthly payment for 5 years ar rate of 6.50% per annum

First we consider that payment is monthly, so the rate should convert to monthly

Monthly rate = 6.50% / 12 = 0.54166666%

After use the formula

PV =   A *   ( 1 -   ( 1 / (1 + r )^n ) )   /   r

Where,

PV = present value = $ 26750

A = monthly payment = to find ?

R = rate (monthly ) = = 0.54166666%

N = number of periodic payment total = 12 months in 5 years = 60

Put the values in to the formula

26750 = A * ( ( 1 – ( 1 / ( 1 + 0.54166666% )^60 ) ) /     0.54166666% )

26750 = A * ( ( 1 – 1 / 1.3828 ) / 0.54166666% )

26750 = A * ( ( 1 - 0.7232 ) /   0.54166666% )

26750 = A * ( 0.2768 / 0.54166666% )

26750 = A *   51.10867

A =   26750 / 51.10867

A = 523.39

Each amount should be =   $ 523.39