Question

Mortgage Department

Suppose you are the manager of a mortgage department at a savings bank. Under the state usury law, the maximum interest rate allowed for mortgages is 10 percent compounded annually.

Required:

A. If you granted a $50,000 mortgage at the maximum rate for 30 years, what would be the equal annual payments?

B. If the current market internal rate on similar mortgages is 12 percent, how much money does the bank lose by issusing the mortgage described in part(a)?

C. The usury law does not prohibit banks from charging points. One point means that the borrower pays 1 percent of the $50,000 loan back to the lending institiution at the inception of the loan. That is , if one point is charged, the repayments are completed as in part(a), but the borrower receives only $49,5000. How many points must the bank charge to earn 12 percent on the 10 percent loan?

Answer 1

Answer 1: Equal Annual Payments

The equal annual payments for the above transaction would be $5303.96.

Stepwise calculations explained as follows:

Sum mortgaged = $50,000

N (Number of years) = 30 years

Interest Rate = 10%

To calculate Equal Annual Installment, we first need to calculate annuity factor

AF = (1-(1+r)^-n) / r

AF = (1-(1.1)^-30) /.10

AF = (1 - 0.0573)/.10

AF = 9.4269

Now, we can divide principal amount with Annuity Factor = 50000/9.4269 = $5303.96

Answer 2: The money bank loses if Market Internal rate is 12%

Particulars	@10%	@12%
Total receipts by bank	$5303.96*30 = $159,118.8	$6207.18*30= $186,215.4
Total Principal Amount	$50000	$50000
Total Interest Earnings	$109,118.8	$136,215.4

Net loss to bank when mortgage is done at 10% = $136,215.4 - $109,118.8 = $27096.6

Answer 3:

For every point, bank gets back $500 from the borrower, however, the repayments remain the same. Therefore, in order to earn the same, as in case of 12% mortgage loan, the bank should charge points as follows:

Total difference in earnings / Receipt per point

27096 / 500

54 points should be charged to equate the earnings in the both scenarios.