Question

In: Finance

Ana just got a five-year car loan for $40,000 with 6% interest rate (APR) and monthly...

Ana just got a five-year car loan for $40,000 with 6% interest rate (APR) and monthly payments. You explained to her that 6% is too high, and she could have saved a lot of money if she negotiated with the bank and got 3% instead. How much money would your friend have saved every month if the rate was 3% instead of 6%?

Expert Solution

In case of 6% interest rate:

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

Monthly rate = Annual rate/ 12 months

= 6%/ 12 months

= 0.50%

Hence, the monthly rate of interest is 0.50%.

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

Hence, the present value annuity factor is 51.7255607407.

Compute the monthly payment, using the equation as shown below:

Monthly payment = Loan/ PVIFA

= $40,000/ 51.7255607407

= $773.312061333

Hence, the monthly payment is $773.312061333.

In case of 3% interest rate:

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

Monthly rate = Annual rate/ 12 months

= 3%/ 12 months

= 0.25%

Hence, the monthly rate of interest is 0.25%.

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

Hence, the present value annuity factor is 55.6523576751.

Compute the monthly payment, using the equation as shown below:

Monthly payment = Loan/ PVIFA

= $40,000/ 55.6523576751

= $718.747626713

Hence, the monthly payment is $718.747626713.

Compute the monthly savings in loan payment, using the equation as shown below:

Monthly savings = Monthly payment if rate is 6% - Monthly payment if rate is 3%

= $773.312061333 – $718.747626713

= $54.56443462

Hence, the monthly savings in loan payment will be $54.56443462.

jeff jeffy answered 2 years ago

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