A banker can lend money at 9.1% compounded monthly or at 9.3% compounded quarterly. If the length of the loan is 15 years, which type of loan profits the banker more?

The quarterly compounding is more profitable

Explanation:

We will compare the total payment under monthly payment to that under quarterly payment and the choose the higher one.

This is done as follows:

Monthly interest =  9.1%/12 = 0.758

number of months =15 × 12 = 180

Monthly payment = ( 1-1.00758^(-180))/0.00758=98.04

Total payment = 98.04 × 180 =17,647.31

Quarterly compounding

Quarterly interest rate = (9.3%/12)×3 = 2.325 %

number of quarter = 4×15 = 60

Quarterly payment = (1-1.002325^(-60))/0.002325= 374.17

Total payment = 374.17× 60 = $22,449.91

The quarterly compounding produces total repayment  a higher than the monthly. Hence, the quarterly repayment is more profitable