Question

6) A mortgage (loan for buying a house) is an ordinary annuity. With a standard 30-year fixed rate loan, the money is borrowed today and paid back monthly for 30 years in a constant amount. In Yolo County the maximum conforming loan amount is $552,000. A conforming loan meets conditions set by government sponsored entities (GSE) called Fannie Mae and Freddie Mac in the US. Conforming loans usually get a lower interest rate because the bank can sell them easily to the GSEs if they want. Suppose someone borrows $552,000 today to buy a house in Davis, CA. If the annual interest rate with monthly compounding, what should be the fair value monthly mortgage payment? Provide a calculation. Banks will sometimes offer a homebuyer to "buy points". This allows the homebuyer to pay money to the bank today to lower the interest rate on their mortgage. One point is 1% of the borrowed amount. For example from part a), suppose I point would cost $5,520 and reduce the interest rate to 3.75%. Based on the new interest rate, what would be the monthly mortgage payment? This is a tough question. Should the homebuyer take the deal from part b)? Provide a calculation For any calculation that you do you should assume the annual interest rate is 4%. b)

Answer 1

The Monthly Repayment on Loan will be calculated using formula below.

+(1+r)n PMT = P *(1+r)n-1

Answer a)

Principle	$5,52,000.00
Tenure	30 years	360 months
Effective Interest rate	4%	0.333%(monthly)
Repayment	$2,634.06	=5,52,000*[(0.333%(1+0.333%)^360)/(1+0.333%)^360-1)

Answer b)

Principle	$5,52,000.00
Tenure	30 years	360 months
Effective Interest rate	3.75%	0.3125%(monthly)
Repayment	$2,556.40	=5,52,000*[(0.3125%(1+0.3125%)^360)/(1+0.3125%)^360-1)

Answer c)

Repayment in a	$2,634.06
Repayment in b	$2,556.40
Change in repayment	$77.66

Monthly benefit of investment of $ 5520 @ 4% for 30 years.

Investment	5520
Tenure	30 years	360 months
Effective Interest rate	4.00%	0.333%(monthly)
monthly benefit	$26.35

As monthly benefit < Change in repayment ,

So, home buyer should take the deal.