A bank originates $150,000,000 worth of 30-year single-family mortgages funded by demand deposits and the required amount of capital. Reserve requirements are 10 percent and the bank pays 32 basis points in deposit insurance premiums. The bank is earning a 6.25 percent coupon on the mortgages. The mortgages are priced at par and total monthly payments on the mortgages are $923,576.
If the bank can originate and securitize this amount of mortgages with the same terms four times over the next year (including the existing mortgages)and the bank earns a servicing fee each month equal to 3.5 percent of the monthly payments,what will be the bank's monthly fee income 12 months from now?

Question

Quizplus · Accepted Answer

The first step is to calculate the monthly payment on a $150,000,000 mortgage at 6.25% interest over 30 years. Using the PMT function on a financial calculator, we get a monthly payment of $923,576.

Next, we need to calculate the bank's required reserves on the mortgages. Since reserve requirements are 10%, the bank must keep $15,000,000 ($150,000,000 x 10%) in reserves. This means the bank can lend out $135,000,000 ($150,000,000 - $15,000,000) in demand deposits and capital.

The bank pays 32 basis points in deposit insurance premiums, which is equivalent to 0.32% per year. This means the bank pays $480,000 in deposit insurance premiums ($150,000,000 x 0.0032) per year, or $40,000 per month.

The bank earns a servicing fee of 3.5% on the monthly payments, which is $32,360 per month ($923,576 x 0.035).

Over the course of a year, the bank will originate and securitize $600,000,000 ($150,000,000 x 4) in mortgages. Each month, the bank will collect $32,360 in servicing fees on each of these mortgages, for a total monthly servicing fee income of $129,301 ($32,360 x 4).

Therefore, the answer is D) $129,301.

A Bank Originates $150,000,000 Worth of 30-Year Single-Family Mortgages Funded