SOLUTION: Jack intends to buy a house for $454700. He intends to make a 25 percent down payment and amortize the remaining balance for 29 years at 9.96 percent interest compounded monthly. H

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Question 1178680: Jack intends to buy a house for $454700. He intends to make a 25 percent down payment and amortize the remaining balance for 29 years at 9.96 percent interest compounded monthly. How much money would have Michael saved if he amortized the balance for 17 years instead of the original 29 years?
I am not sure how to solve the above question, but I did solve for the information below.
My Work:
I solved the following using the formula P=K[1-(1+i)^(n)/i]
What is his monthly payment? 2999.48
How much will actually be paid for the house? 1157494.04
How much equity does Michael have after 19 years? 227344.95
What would his monthly payments be if Michael amortized the balance for 17 years instead? 3473.95





Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your work looks good so far.

you got:

with a 29 year mortgage:

the monthly payment was 2999.48


he paid 348 * 2999.48 = 1043819.04 total for the mortgage plus the down payment of 113675 = 1157494.04.

the equity that he has after 19 years can be calculated as follows:

19 * 12 = 228 months.
348 months minus 228 months = 120 months.
find the present value of the monthly payment of 2999.48 at the same interest rate for 120 months to get a present value of 227355.05.

this is a little bit off but comparable to your calculations.

with a 17 year mortgage, his monthly payments were 3473.95.

your calculations are correct for this.

his total payments for the 29 year mortgage were 348 * 2999.48 = 1043819.04
his total payments for the 17 year mortgage were 204 * 3473.95 = 708685.8
he saved the difference.
that was equal to 1043819.04 minus 708685.8 = 335133.24

since the down payment was the same in both scenarios, they didn't figure into the calculations for the difference.

i think that answers your questions.
let me know if you need more.