SOLUTION: Your annual income is $50,000. You want to take out a mortgage loan to buy a house. The rule on mortgage loan requires that your annual mortgage payment cannot exceed 30% of your a

Question 886768: Your annual income is $50,000. You want to take out a mortgage loan to buy a house. The rule on mortgage loan requires that your annual mortgage payment cannot exceed 30% of your annual income. If the current interest rate is 5% for a 30-year mortgage loan, what is the maximum amount one can borrow for a house?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
income is $50,000
annual mortgage payment cannot exceed 30% of your annual income.
current interest rate is 5% per year for a 30 year mortgage loan.

30% of $50,000 = $15,000 which is the most payments you can make per year on the mortgage.

since mortgage payments are made monthly, divide that $15,000 by 12 and you get a maximum payment of $1250.00 per month.

interest rate of 5% per year becomes interest rate of 5% / 12 = .41666666667% per momnth.

number of months becomes 30 * 12 = 360 months.

your payment cannot exceed $1250.00 per month.

present value of a monthly payment of $1250.00 for 360 months at .4166666667% per month would be equal to $232,852.

that is the maximum mortgage the bank will allow you.

to solve this problem you need to find the formula for the present value of a payment which is also called the present value of an annuity.

you also need to put everything in months since mortgages are typically paid per month.

you divide the interest rate by 12 and you multiply the number of years by 12.
the interest rate is the interest rate percent divided by 100.

http://www.investopedia.com/articles/03/101503.asp

in this reference you are looking for the formula for PV of an ordinary annuity.

i assumed months.
if you are working in years, then the problem becomes different.
your maximum payment is still $15,000 per year.
your payments are $15,000 a year for 30 years.
this would come out to be a present value of a payment of $15,000 for 30 years at 5% interest which would be equal to $230,587.
that would be your maximum mortgage if you paid once a year and the interest was compounded once per year.

you use the same PV of an ordinary annuity formula but pmt is now $15,000 and interest rate is now .05 and number of time periods is now 30.

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