Question

Imagine that you are a banker getting a loan ready for a client, Jama Hamza. They are buying a 1700 square foot home for the price of $374,500. In order to avoid PMI, Abdi puts 10% of the price as a down payment. He qualifies for 5.68% annual interest rate for a 30 year loan.

Round all answers to the nearest cent.

• Jama also qualifies for a 15 year loan at an annual rate of 4.2%. How much money would he save on interest if he took this loan instead of the 30 year loan?                               
• Most lenders will approve a home loan if the total of all the borrower’s monthly payments, including the home loan is no more than 38% of the borrower’s total monthly income. How much must Jama make in order to qualify for the loan?

Answer 1

Home Price = $374,500

Loan amount after down-payment = $374,500*(1-10%)

= $337,050

- Calculating the Monthly payment of loan if Jama takes a 30-year loan:-

Where, P = Loan Amount = $337,050

r = Periodic Interest rate = 5.68%/12 = 0.47333%

n= no of periods = 30 years*12 =360

Monthly Payment = $1951.97

Total Interest on Loan = ($1951.97*360) - $337,050

= $365,659.20

- Calculating the Monthly payment of loan if Jama takes a 15-year loan:-

Where, P = Loan Amount = $337,050

r = Periodic Interest rate = 4.2%/12 = 0.35%

n= no of periods = 15 years*12 =180

Monthly Payment = $2527.03

Total Interest on Loan = ($2527.03*180) - $337,050

= $117,815.40

Interest saved by JAMA over 15-year loan instaed of 30-year loan = $365,659.20 - $117,815.40

= $247,843.80

So, JAMA saved $247,843.80 in Interest.

b)

Loan will be approved if JAMA's monthly payment including home loan is no more than 38% of monthly income.

Monthly Income of JAMA must be = 30-year monthly loan payment/38%

= $1951.97/38%

= $5136.76

So, Jama must make in order to qualify for the loan is $5136.76