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.

• Create an amortization table for the first 3 months of the 30 year loan.          
• Jama has asked for ideas that might help him pay the loan off early. As his financial advisor, give two pieces of advice you can give him in order to pay the loan off early. They should be reasonable and not a large financial strain.

Answer 1

Cost of the house = $374,500

Down payment = 10% of cost of house or 10% of $374,500 = $37,450

Therefore, loan amount = Cost of the house - Down payment

= $374,500 - $37,450 = $337,050

We can use resent value (PV) of an Annuity formula to calculate the equal monthly payment of mortgage loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV of mortgage loan = $337,050

PMT = Monthly payment =?

n = N = number of payments = 30 years *12 months =360 month

i = I/Y = 5.68% per year, therefore monthly interest rate = 5.68%/12 = 0.4733% per month

Therefore,

$337,050 = PMT* [1- (1+0.005313)^-360]/0.005313

= $1,951.97

Monthly payment is $1,951.97 for this mortgage loan    

Amortization table for the first 3 months of the 30 year loan

Loan amount	$337,050.0
Monthly payment =	$1,951.97
Monthly Interest rate =	0.4733%
Time period (months) =	360
Amortization Schedule
Month	Beginning Balance	Total payment (PMT)	Interest Payment @ 0.4733% of beginning balance	Principal payment (Total Payment - Interest)	Ending Balance (Beginning balance - Principal Payment)
1	$337,050.0	$1,951.97	$1,595.37	$356.60	$336,693.40
2	$336,693.40	$1,951.97	$1,593.68	$358.29	$336,335.11
3	$336,335.11	$1,951.97	$1,591.99	$359.98	$335,975.13

If Jama wants to pay the loan off early then two pieces of advice to him in order to pay the loan off early are-

1. He can increase his monthly payment amount, this way he will pay more proportion of principal amount and can pay the loan off early

2. He can pay more in down payment instead of 10% so the loan amount will be lessor and by paying the above calculated monthly payment, he can pay the loan off early

Formulas used in excel calculation: