Question

Darla purchased a new car during a special sales promotion by the manufacturer. She secured a loan from the manufacturer in the amount of $24,000 at a rate of 4.9%/year compounded monthly. Her bank is now charging 6.3%/year compounded monthly for new car loans. Assuming that each loan would be amortized by 36 equal monthly installments, determine the amount of interest she would have paid at the end of 3 years for each loan. How much less will she have paid in interest payments over the life of the loan by borrowing from the manufacturer instead of her bank? (Round your answers to the nearest cent.)

interest paid to manufacturer	$
interest paid to bank	$
savings

Answer 1

Under compound interest, the interest per period is paid on the principal balance plus any outstanding interest already accrued ie Interest on interest.

Interest paid to manufacturer:-

Principle=$24,000

Rate of interest 4.9%/ year of 0.40833% per month

Period= 36 months

Calculate R ie. Periodic payment:

R= Principle x interest rate/ 1-(1+Interest rate)^{-number of installmets}

R= 24000 X 0.004083 / 1-(1+0.004083)^-36

R= 24000 X 0.004083 / 1-(1+0.004083)^-36

R=$718

Total amount paid in 36 installments

36 X $718

$25856

Calculate Interest paid=

$25856-$24000

$1856

B. Interest paid to Bank:-

Principle=$24,000

Rate of interest 6.3%/ year of 0.525% per month

Period= 36 months

Calculate R ie. Periodic payment:

R= Principle x interest rate/ 1-(1+Interest rate)^{-number of installmets}

R= 24000 X 0.00525 / 1-(1+0.00525)^-36

R= 24000 X 0.00525 / 1-(1+0.00525)^-36

R=$733.40

Total amount paid in 36 installments

36 X 733.40$

$26402

Calculate Interest paid=

$26402.4-$24000

$2402

Thus savings in interest=

$2402-$1856

$546