Question

# Rosa bought a car for \$20,000. She made a down payment of \$4,000 and received a...

Rosa bought a car for \$20,000. She made a down payment of \$4,000 and received a 48-month equal installment loan for the remaining amount at 6 percent APR. How much will be Rosa’s first payment of the loan? (Assume the installments are paid at the end of each month.) Group of answer choices

\$1277.95

\$469.70

\$333.33

\$ 375.76

Solution

Loan amount=Purchse price of car-Downpayment=20000-4000=16000

Now this is an ordinary annuity and the formula for present value of annuity is given below

Present value of annuity=Loan amount=Annuity payment*((1-(1/(1+i)^m))/i)

where

i-discount or intrest rate per period-6/12=.5% per month

m-number of periods =48

Present value of annuity =Loan amount=16000

Annuity payment=Monthly payment=?

Putting values in formula

Present value of annuity=16000=Annuity payment*((1-(1/(1+.005)^48))/.005)

Solving we get

Annuity payment(Monthly payment)=\$375.76

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