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 a 5.68% annual interest rate for a 30-year loan.

Round all answers to the nearest cent.

- Find the amount of Jama’s monthly payment. Use the formula from class and show your work. You may check your answer with Excel.
- If Jama does not make any extra payments find the total amount of money that he paid for his home and determine the interest that the bank will make on the loan. Assume the last payment is the same as the first and the balance is paid off completely with the last payment.

Answer #1

**Monthly
Loan Payment**

Loan Amount (P) = $337,050 [$374,500 x 90%]

Monthly interest rate (n) = 047333333% per month [5.68% / 12 Months]

Number of period (n) = 360 Years [30 Years x 12 Months]

Therefore, the monthly loan payment
= [P x {r (1 + r)^{n}} ] / [(1 + r)^{n} – 1]

= [$337,050 x {0.0047333333 x (1 +
0.0047333333)^{360}}] / [(1 + 0.0047333333)^{360} –
1]

= [$337,050 x {{0.0047333333 x 5.473837261}] / [5.473837261 – 1]

= [$337,050 x 0.025909496] / 4.473837261

= $8,732.80 / 4.473837261

= $1,951.97

Monthly Payment is $1,951.97

**Total Loan Payment**

Total Loan Payment = $1,951.97 per month x 360 Months

= $702,709.20

Total Loan Payment is $702,709.20

**Total Interest Payment**

Total Interest Payment = Total loan payment – Loan amount

= $702,709.20 - $337,050

= $365,659.20

Total Interest payment is $365,659.20

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