Jake buys a $140,000 home. He must make monthly mortgage payments for 40 years, with the first payment to be made a month from now. The annual effective rate of interest is 8%. After 20 years Jake doubles his monthly payment to pay the mortgage off more quickly. Calculate the interest paid over the duration of the loan.

• $241,753.12
• $527,803.12
• $356,440.43
• $136,398.99
• $225,440.43

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Solution: E

Monthly rate of interest: [math]j=(1+.08)^{1 / 12}=.00643[/math]

[[math]] \begin{aligned} & 140,000=x a_{\overline{480}| .00667 }\\ & x=927.513 \end{aligned} [[/math]]

outstanding balance after 20 years

[[math]] 927.513=\mathrm{a}_{\overline{480} | .00667}=114,611.417 [[/math]]

doubling the payments:

[[math]] 927.513(2)=1855.03 [[/math]]

new amount of years:

[[math]] \begin{aligned} & 114,611.417=1855.03 \mathrm{a}_{\overline{n}| .00667} \\ & \mathrm{n}=76.916=77 \end{aligned} [[/math]]

total paid

[[math]] 927.513(240)+1855.03(77)=365,440.43 [[/math]]

interest

[[math]] 365,440.43-140,000=225,440.43 [[/math]]

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.