homeowener is considering refinancing his home. original amount of the 30 yr loan was 250,000 at 12% compounded monthly. The owner has made ten years of payments. how much is the remaining balance on the loan.

Question

this is what I gotL

r=12%, m=12, i=12%/12=1%/month

I have to find out the annual payments he made so I did: A=P(A/P,i,n)
A=250,000(A/P,i,n)
using the percentage table, I get A.

Then how do I solve for the future value or also known as the balance.

Answer 1

An excel spreadsheet is very good for these kinds of problems. Unfortunately, this problem will contain an ugly 'sum' part.
(Finance guys are into these look-up tables, which appears to be the path you are heading. I prefer using math and an excel spreadsheet -- )

First thing I would do is solve for P. Find P such that the balance of the loan after 360 payments is zero.
We know B0 = 250000.
B1 would therefore be B0*(1+.12/12) - P = B0*1.01 - P
(That is, the balance changes by the interest hit, but is reduced by the constant payment). Continuing:

B2 = B1*(1.01) - P
+ B0*(1.01)^2 - P*1.01 - P
So, by extension
Bn = B0*(1.01)^n - P*(1.01^(n-1) + 1.01^(n-2) + ... 1.01^0)

We also know that Bn = B360 = 0 (the loan is paid off). So use the above equation to solve for P.

So, now you have everything you need.
(And if you used excel, your answer would appear in one of the cells)

B120 = B0*(1.01)^120 - P*(1.01^119 + 1.01^118 + ... 1.01^0)