Your brother has decided to purchase a new automobile with a hybrid-fueled engin

Question

Your brother has decided to purchase a
new automobile with a hybrid-fueled engine
and a six-speed transmission. After the trade-in of his
present car, the purchase price of the new automobile
is $30,000. This balance can be financed by the auto
dealership at 2.9% APR and payments over 48 months.
Compounding of interest is monthly. Alternatively, he
can get a $2,000 discount on the purchase price if he
finances the loan balance at an APR of 8.9% over 48
months. Should your brother accept the 2.9% financing
plan or accept the dealer’s offer of a $2,000 rebate with
8.9% financing?

Explanation / Answer

Purchase price of the new automobile =$30,000.=P

Interest rate =2.9%.=i

Tenor of the loan=48 months.=n

Interest compounding is done monthly.

Formula for determining the monthly instalment =(Principal * interest rate)/[1-(1+i)-n]

Substituting the values in the formula =($30,000* 2.9%)/[(1-(1+.029)-48)

=$1,165.52.

Second option:

Purchase price =$30,000.

As the payment is made in cash by taking a loan discount=$2,000.

Effective loan amount=$28,000.=PV

Interest rate=8.9%/12.=.089/12 = i

Tenor of the loan=48 months.=nper

Loan Installment is calculated by using PMT function in Excel.

PMT(rate,nper,pv) =PMT(.089/12,48,-28,000)

=$695.45.

As, the instalment is less in the case of $2,000 rebate, dealer's offer should be accepted.

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