Question 321987: The price of a home is $150,000.00. The bank requires 15% down payment. The
buyer is offered 2 mortgage options. 15-year fixed at 9.5% or 30-year fixed at
9.5%.
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?
Help, these problems drive me crazy!!! Thank you!!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Price of a home is $150,000.
Bank require 15% down payment.
15% of 150,000 = $22,500
150,000 minus 22,500 = 127,500
That's the amount you have to mortgage.
You have 2 mortgage options.
Option 1 is a 15 year fixed mortgage at 9.5%.
Option 2 is a 30 year fixed mortgage at 9.5%
Both mortgages give you the same interest rate.
The only difference is in the amount of time required to pay off the loans.
I used a financial calculator to give you the answers to these problems.
If you need formulas, I can provide them, but I won't go to that trouble unless you absolutely need them to solve these problems.
You can use online mortgage calculators to provide you with the same answer.
Here's the answers.
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Option 1 is a 15 year mortgage at 9.5% per year.
Since a mortgage is normally paid monthly and normally paid at the end of each month, then the calculator is set to do that after we modify the inputs as follows:
Number of periods in the loan = 15 * 12 = 180
Interest Rate per period is 9.5% / 12 = .791666667%
Present Value of the loan is $127,500
Plugging those numbers into the calculator gives a monthly payment of $1,331.386471.
The total payments made on this loan are 180 * $1,331.386471 = $239,649.5648
The principal of this loan is $127,500.
Total interest paid on this loan is $239,649,5648 - $127,500 = $112,149.5648
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Option 2 is a 30 year mortgage at 9.5% per year.
Since a mortgage is normally paid monthly and normally paid at the end of each month, then the calculator is set to do that after we modify the inputs as follows:
Number of periods in the loan = 30 * 12 = 360
Interest Rate per period is 9.5% / 12 = .791666667%
Present Value of the loan is $127,500
Plugging those numbers into the calculator gives a monthly payment of $1,072.089114
The total payments made on this loan are 360 * $1,072.089114 = $385,952.081
The principal of this loan is $127,500.
Total interest paid on this loan is $385,952.081 - $127,500 = $258,452.081
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By taking the 15 year option, the buyer saves a total of $$258,452,081 interest from the 30 year mortgage minus $112,149.5648 from the 15 year mortgage which equals a total savings in interest of $146,302.5162.
Whether the buyer should take the 15 year mortgage or the 30 year mortgage has to do with affordability and alternate investment opportunities that I won't get into now because they would detract too much from the questions that you were asked to answer.
If you have to use formulas, and you don't have them, let me know and I'll send you copies of what I have.
You should get the same answers but you will work a lot harder to find them.
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