# Calculus

A \$99,000 mortgage for 30 years at 9% APR requires monthly payments of \$796.58. Suppose you decided to make monthly payments of \$1,100. When would the mortgage be completely paid?

I am using a present value of annuity eguation but don't know how to solve for time.

Can you use logs?
Remember that log a^n= n*log a and you can solve for n in that.

thats what i forgot.
thanks for the help

The value of an annuity usually depends upon the expected remaining years of life of the beneficiary. If the annuity pays out a fixed monthly amount for a specified period, then the formula to use would be the same as amortization. You need an amortization calculator.
The formula is:

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

Where:

A = periodic payment amount

P = amount of principal

i = periodic interest rate

n = total number of monthly payments

In your case you want to solve for n, so an interative technique or spreadsheet approach may be required.

Using a mortgage calculatorm at this website,
http://mortgages.interest.com/content/calculators/monthly-payment.asp
I get a payoff period of 12.5 years if the monthly payment is 1101.66 and the interest rate is 9%. It will be a month longer if you pay \$1100.

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