Question

The price of a home is ​$240 000. The bank requires a​ 15% down payment. The buyer is offered two mortgage​ options: 15-year fixed at 8.5​% or​ 30-year fixed at 8.5​%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the​ 15-year option? Use the following formula to determine the regular payment amount. Find the monthly payment for the​ 15-year option. ​$ nothing ​(Round to the nearest dollar as​ needed.) Find the monthly payment for the​ 30-year option. ​$ nothing ​(Round to the nearest dollar as​ needed.) Calculate the total cost of interest for both mortgage options. How much does the buyer save in interest with the​ 15-year option? ​$ nothing ​(Use the answers from parts 1 and 2 to find this​ answer.)

Answer 1

1)

Formula for EMI is:

EMI = P × r × (1 + r) ⁿ / {(1 + r) ⁿ - 1}

Where,

P = Principal of loan = $ 240,000 – (1- 0.15) = $ 240,000 x 0.85 = $ 204,000

r = rate of interest = 8.5 % p.a. or 0.08/12 or 0.007083333 monthly

n = No. of periods = 15 years x 12 months = 180 periods

EMI = $ 204,000 x 0.007083333 x (1 + 0.007083333)¹⁸⁰ / {(1 + 0.007083333) ¹⁸⁰ -1}

        = $ 204,000 x 0.007083333 x (1.007083333)¹⁸⁰ / {(1.007083333) ¹⁸⁰ -1}

        = $ 204,000 x 0.007083333 x 3.562653123 / (3.562653123-1)

        = $ 204,000 x 0.007083333 x 3.562653123 / 2.562653123

        = $ 204,000 x 0.007083333 x 1.390220585

        = $ 2,008.868651 or $ 2,009

Monthly payment for 15 years loan is $ 2,009

2)

Let’s compute EMI for 30 year loan

n = 30 years x 12 months = 360 periods

EMI = $ 204,000 x 0.007083333 x (1 + 0.007083333)³⁶⁰ / {(1 + 0.007083333) ³⁶⁰ -1}

        = $ 204,000 x 0.007083333 x (1.007083333)³⁶⁰ / {(1.007083333) ³⁶⁰ -1}

        = $ 204,000 x 0.007083333 x 12.6924972747/ (12.6924972747-1)

        = $ 204,000 x 0.007083333 x 12.6924972747/ 11.6924972747

        = $ 204,000 x 0.007083333 x 1.0855249291

        = $ 1,568.5834486818 or $ 1,569

Monthly payment for 30 years loan is $ 2,009

3)

Total payment for 15 year loan = 180 x $ 2,009 = $ 361,620

Interest amount = Total payment – Principal = $ 361,620 - $ 204,000 = $ 157,620

Total payment for 30 year loan = 360 x $ 1,569 = $ 564,840

Interest amount = Total payment – Principal = $ 564,840 - $ 204,000 = $ 360,840

Difference in interest = $ 360,840 - $ 157,620 = $ 203,220

The buyer can save $ 203,220 in interest with the​15-year option.