Question

Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR)

of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?
$104.54
$378.21
$450.71
$1225.56

Answer 1

The monthly payment is $450.71

Explanation:

Financial Computing

Given the loan amount A, the loan term t, and the APR (annual percentage rate), the montly payment is computed as

`\displaystyle P=(A)/(f)`

where f is

`\displaystyle f=(1-(1+i)^(-n))/(i)`

The provided data is

`\displaystyle A=24,000`

`\displaystyle r=4.8\%`

`\displaystyle t=5\ years`

Since the payments will be made monthly, the values of n and i are:

`\displaystyle i=(4.8)/(100*12)=0.004`

`\displaystyle n=5*12=60\ months`

Calculating f:

`\displaystyle f=(1-(1+i)^(-n))/(i)`

`\displaystyle f=(1-(1+0.004)^(-60))/(0.004)`

`\displaystyle f=53.25`

Now for the payments:

`\displaystyle P=(24.000)/(53.25)=450.71`

`\boxed{\displaystyle P=\$450.71}`