Answer:
- $1065.15
- $687.48
- $55,764.98
Step-by-step explanation:
1) The payment can be found using a financial calculator, spreadsheet, or the amortization formula:
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the loan amount, r is the annual interest rate, n is the number of times per year interest is compounded, t is the number of years.
Since a 10% down payment was made, the amount of the loan is ...
$160,000 - 10%×$160,000 = $144,000
For 4% interest compounded monthly for 15 years, the monthly payment is ...
A = $144,000(0.04/12)/(1 -(1 +0.04/12)^(-12×15)) ≈ $1065.150613
The monthly payment for the 15-year loan is $1065.15.
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2) Using the same formula for the 30-year loan, we find the payment to be ...
A = $144,000(0.04/12)/(1 -(1 +0.04/12)^(-12×30)) ≈ $687.478025
The monthly payment for the 30-year loan is $687.48.
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3) The total of the payments on the 15-year loan is ...
180×1065.150613 = $191,727.11
The total of payments on the 30-year loan is ...
360×$687.478025 = $247,492.09
The difference of these amounts is the interest savings with the 15-year option:
$247,492.09 -191,727.11 = $55,764.98
The buyer saves $55,764.98 in interest with the 15-year option.
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<em>Comment on interest savings</em>
For part 3, the difference between 180 of the given payments and 360 of the given payments is $55,765.80 (interest savings), slightly more than shown above. The reason we did the calculation with extra decimal places was to approximate the actual amount paid. There is usually a slight adjustment in the last payment to make up the difference caused by rounding payment values to the penny. If you were to actually work out the numbers, rounding after each payment, you would probably get a result somewhere between these values.
