The price of a home is $160,000. the bank requires 10% down payment. the
buyer is offered 2 mortgage options. 15-year fixed at 4% or 30-year fixed at
4%.
1) find the monthly payment for the 15-year option.
2) find the monthly payment for the 30-year option.
3) calculate the total cost of interest for both mortgage options. how much does the buyer save in interest with the 15-year option?

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.

Comment on interest savings

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.

nlgqer

step-by-step

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step-by-step explanation: