Math
posted by Yolanda on .
My monthly mortgage payments are $4,369.66 for 30 years at 8%, what is the original cost of the house?

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)^(n1)+A(1+i)^(n2)...+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+i1)
=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]