Question

A man buys a car for $40,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $600 for 60 months, how much must he put down? (Round your answer to the nearest cent.)

Answer #1

Compute the monthly interest rate, using the equation as shown below:

Monthly rate = Annual rate/ 12 months

= 12%/ 12 months

= 1%

Hence, the monthly rate is 1%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)^-Number of periods}/ Rate

= {1 – (1 + 0.01)^-60}/ 1%

= 44.9550383968

Hence, the present value annuity factor is 44.9550383968.

Compute the present value of the loan, using the equation as shown below:

Present value = Monthly loan payment*PVIFA

= $600*44.9550383968

= $26,973.02

Hence, the present value of loan is $26,973.02.

Compute the down payment amount, using the equation as shown below:

Down payment = Car price – Present value of loan

= $40,000 – $26,973.02

= $13,026.98

Hence, the down payment amount is $13,026.98.

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