Calculus

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Finance

    You take out a 30-year $100,000 mortgage loan with an APR of 6 percent and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?
  2. Finance

    You take out a 30-year $100,000 mortgage loan with an APR of 6 percent and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?
  3. math

    The Johnsons have accumulated a nest egg of $19,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided …
  4. finance

    You take out a 25-year $210,000 mortgage loan with an APR of 12% and monthly payments. In 16 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?
  5. Maths

    Mortgage company lets you pay a point (1% of total amount of loan)to reduce APR from 6.5% to 6.25% on a $400,000 30-yr mortgage with monthly payments. Plan to be in house for at least five years. Should you pay the point?
  6. Finance

    A mortgage broker is offering a $225,000 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 2.5 percent APR interest rate. After the second year, the mortgage …
  7. Finance

    Here's another way to look at it. Suppose you want to borrow $100,000. You choose a 30-year fixed rate loan at 7.5%, and pay one discount point ($1,000), a 1% origination fee ($1,000), and $350 in other fees. Although the lender is …
  8. Math

    A mortgage of 200 000 is required to purchase a house. The mortgage will be repaid with equal monthly payments over 25 years at 10% compounded monthly. what is the monthly payment
  9. Finance

    Ron starts with a $100,000 mortgage at 8% for 30 years, annual payments. Ten year into the mortgage Ron is able to refinance the balance of the mortgage at 6%. a) If he chooses to refinance for 20 years what would his new payments …
  10. Finance

    Ron starts with a $100,000 mortgage at 8% for 30 years, annual payments. Ten year into the mortgage Ron is able to refinance the balance of the mortgage at 6%. a) If he chooses to refinance for 20 years what would his new payments …

More Similar Questions