Your brother-in-law asks you to lend him $100,000 as a second mortgage on his vacation home. He promises to make level monthly payments for 10 years, 120 payments in all. You decide that a fair interest rate is 8% compounded annually. What should the monthly payment be on the $100,000 loan?

• $1060
• $1079
• $1099
• $2010
• $2020

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

Solution: C

The fair monthly rate is [math](1+0.08)^{1 / 12}-1=0.006434[/math]. Let C be the appropriate monthly payment. Then,

[[math]]\frac{C}{0.006434}\left[1-\frac{1}{1.006434^{120}}\right]=100,000.[[/math]]

C=$1,198.58.

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.