Suppose that you decide to borrow 16000 for a new car. You can select one of the following loans each requiring regular monthly payments. Installment  loan A three-year loan at 6.3%Installment  loan B  five -year loan at 6.4%What would be the monthly payments for each loan and total interest for them also? How much will the buyer save in interest?

Question
Asked Nov 19, 2019
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Suppose that you decide to borrow 16000 for a new car. You can select one of the following loans each requiring regular monthly payments. 

Installment  loan A three-year loan at 6.3%

Installment  loan B  five -year loan at 6.4%

What would be the monthly payments for each loan and total interest for them also? How much will the buyer save in interest?

 

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Expert Answer

Step 1

Loan A has a term of 3 years with 6.3% interest.

The formula to calculate monthly payment is given below:

mxp)
1
1+
Loan amount Monthly paymentx
р
Here
i is interest rate
p is number of payment in a year
n is number of years
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mxp) 1 1+ Loan amount Monthly paymentx р Here i is interest rate p is number of payment in a year n is number of years

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Step 2

Substitute 6.3% for i, 12 for p and 3 for n, and $16,000 for loan amount,

-(3x12)
6.3%
1+
12
$16,000 Monthly payment x
6.3%
12
-36
1-(1+0.525%)
Monthly payment x
$16,000
0.525%
0.17818
$16,000 Monthly payment x
0.525%
$16,000
Monthly payment x 32.72459777
$16,000
Monthly payment
32.72459777
$488.92 Monthly payment
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-(3x12) 6.3% 1+ 12 $16,000 Monthly payment x 6.3% 12 -36 1-(1+0.525%) Monthly payment x $16,000 0.525% 0.17818 $16,000 Monthly payment x 0.525% $16,000 Monthly payment x 32.72459777 $16,000 Monthly payment 32.72459777 $488.92 Monthly payment

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Step 3

Total interest paid on the loan...

Total interest
Total payment - Loan amount
(Monthly payment x T otal number of payment)
-Loan amount
=($488.92x 36) $16,000
$17,601.12-$16,000
$1, 601.12
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Total interest Total payment - Loan amount (Monthly payment x T otal number of payment) -Loan amount =($488.92x 36) $16,000 $17,601.12-$16,000 $1, 601.12

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