Question

Hunan bought a car priced at $15,700 for 15% down and equal monthly payments for four years. If interest is 6% compounded monthly, what is the size of the monthly payment?

The monthly payment is $______
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

$313.41

Explanation:

The formula for calculating the monthly payment on a loan for a certain number of years when compounded monthly is given by:


`PMT = (PV \cdot i \cdot (1 + i)^n)/((1 + i)^n -1)`

Here
PV = loan amount

i = interest rate per month in decimal

n = number of months

We have the value of the car as $15,700. However Hunan paid 15% down so the actual loan amount is 85% of the value = 15,700 x 0.85 = $13,345.00

The annual interest rate is 6% = 6/100 = 0.06 in decimal
Monthly interest rate = 0.06/12 = 0.005

Number of months = 4 years x 12 = 48 months

Plugging in these values into the formula gives

`PMT=(13345 \cdot (0.005) \cdot (1 + 0.005)^(48))/((1 + 0.005)^(48) -1)\\\\ = (13345 \cdot (0.005) \cdot (1.005)^(48))/((1.005)^(48) -1)\\\\\\= 313.41`

So the monthly payment is $313.41

Just use a calculator which can compute the monthly payment given all the values. There are plenty on line