Question

On December 31, 1995, a house is purchased with the buyer taking out a 30-year $90,000 mortgage at 9% interest compounded monthly. The mortgage payments are made at the end of each month. Calculate the amount of the monthly payment.

Answer 1

Answer:

$M = 90000 (\frac{0.0075 (1+0.0075)^{360}}{(1+0.0075)^{360} -1})$

$M = 724.16$

So on this case the reasonable value for the 30 year mortgage monthly payment would be 724.16

See explanation below.

Explanation:

For this case we can use the fomrula for the amortized mortgage payment given by:

$M = P (\frac{i (1+i)^n}{(1+i)^n -1})$

Where:

M represent the monthly payment

P=90000 represent the mortage principal

I = represent the monthly interest, on this case i = 0.09/12= 0.0075. Because is not appropiate use i =0.09 for this case since we got a value of 8100 for the PMT (monthly payment), and this value not makes sense at all.

n = 12*30 =360 represent the number of periods or months on this case

As we can see we have everything in order to replace, so we have this:

$M = 90000 (\frac{0.0075 (1+0.0075)^{360}}{(1+0.0075)^{360} -1})$

$M = 724.16$

So on this case the reasonable value for the 30 year mortgage monthly payment would be 724.16