Posted by **Yolanda** on Monday, June 17, 2013 at 11:18pm.

My monthly mortgage payments are $4,369.66 for 30 years at 8%, what is the original cost of the house?

- Math -
**MathMate**, Tuesday, June 18, 2013 at 7:08am
We need to know how often interest is accrued. It is not always equal to the payment frequency. Some banks compound every 3 months, some six months, and some a year.

For lack of information, we will assume that interest is compounded monthly, which simplifies the calculations.

To do the calculations, we assume:

A=amount of payment per period (month) = $4369.66

P=principal, amount borrowed

i=interest per period (month)=0.08/12

n=number of periods (month) = 30*12=360

We equate the future value of the amount borrowed and the future value of the payments, as follows:

The first payment is assumed to be made at the end of the first period.

P(1+i)^n

=A(1+i)^(n-1)+A(1+i)^(n-2)...+A(1+i)^1+A(1+i)^0

The last term represents the last payment.

The right hand side factorizes to:

A((1+i)^n -1)/(1+i-1)

=A((1+i)^n -1)/i

So the whole equation becomes:

P(1+i)^n=A((1+i)^n -1) /i

Which means that

P=A((1+i)^n -1)/[i×(1+i)^n]

## Answer This Question

## Related Questions

- Math - A mortgage of 200 000 is required to purchase a house. The mortgage will ...
- Math - If my monthly mortgage payments for a house that costs $132, 905. The ...
- Math - Personal Finance - Ina is negotiating a mortgage of $145 000 for her new ...
- Finance - Rob and laura wish to buy a new home. The price is $187,500 and they ...
- accounting - House mortgage You have just purchased a house and have obtained a...
- Finance - You take out a 30 year $100000 mortgage loan with an apr of 6% and ...
- finance - You take out a 25-year $210,000 mortgage loan with an APR of 12% and ...
- cis - 1. Find a mortgage loan calculator to determine what your monthly payments...
- Finance - You take out a 30-year $100,000 mortgage loan with an APR of 6 percent...
- math - The Johnsons have accumulated a nest egg of $19,000 that they intend to ...

More Related Questions