# A lender requires that monthly mortgage payments be no more than 25% of your gross monthly income...

## Question:

A lender requires that monthly mortgage payments be no more than 25% of your gross monthly income with a maximum repayment period of 30 years. If you can make a 15% down payment, what is the minimum monthly payment needed when the interest rate is 6% compounded monthly?

## Mortgage Payments:

A mortgage payments are part of a planned installment agreement between a borrower and a money lender, such as a bank. In addition to the principal (remaining cost of the home after the downpayment) and interest, monthly mortgage payments typically include property and private mortgage insurance premiums and property taxes.

For the purpose of this question, let's assume that the cost of house is $300,000. • Present value (PV) of the mortgage loan = 300,000 * (1 - 0.15) =$255,000
• Annual interest rate = 6%
• Tenure of loan (nper) = 30 years (360 months)

The monthly interest rate can be calculated as follows:

• Rate (r) = 6% / 12
• Rate (r) = 0.5%

We can calculate the monthly payment (pmt) by using the Excel function: PMT(rate, nper, pv,):

Monthly repayment = Pmt(0.5%,360,-255000)= $1,528.85. As per the question, the monthly mortgage repayments can't be any more than 25% of the gross monthly income. Therefore: • Gross Monthly income =$1,528.85 / 25%
• Gross Monthly Income = \$6,115.42 