This Exam FM sample reference tests Mortgage with Extra Payments. The payoff therefore occurs on the next scheduled payment date corresponding to December 31, 2020. The result agrees with the published answer key, choice C.
How to solve this Mortgage with Extra Payments question
Setup
Setup
Compute the original 360-month mortgage payment at 0.5% per month. Treat the extra payments as a separate cash-flow stream and find their time-0 present value.
R=200000/a360∣0.005=1199.10
Model
Model
Subtracting that value from the original principal leaves 158,070.46 to be amortized by the regular payment. Solving the annuity equation gives 215.78 regular-payment months.
PV0(extra payments)=41929.54
Compute
Compute
The payoff therefore occurs on the next scheduled payment date corresponding to December 31, 2020.
158070.46=1199.10an∣0.005⟹n=215.78
Answer
Answer
The calculation gives December 31, 2020 for mortgage with extra payments, matching published choice C.
December 31, 2020(C)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (July 31, 2013) does not match the checked mortgage with extra payments result (December 31, 2020); no distinct standard one-step error is identifiable.
BChoice B (November 30, 2020) does not match the checked mortgage with extra payments result (December 31, 2020); no distinct standard one-step error is identifiable.
DChoice D (December 31, 2021) does not match the checked mortgage with extra payments result (December 31, 2020); no distinct standard one-step error is identifiable.
EChoice E (January 31, 2022) does not match the checked mortgage with extra payments result (December 31, 2020); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: mortgage term reduction from a fixed monthly overpayment
A 200,000 mortgage is amortized over 360 months at 6% nominal interest convertible monthly. Beginning with the first payment, the borrower pays 100 more than the scheduled monthly amount. Calculate the number of whole scheduled months eliminated; use the first month in which the balance is fully repaid.
A 48 months
B 55 months
C 65 months
D 69 months
E 76 months
Variant answer in brief
The equation gives 294.46 months, so payoff occurs in month 295 and eliminates 65 scheduled months. The mortgage term is shortened by 65 months, which is choice C.
Setup
Setup
Calculate the scheduled payment, then add 100 to form the actual monthly payment.
R=200000/a360∣0.005=1199.101050
Model
Model
Solve the annuity equation for the real-valued payoff term and round up because a partial final month is still a payment month.
200000=(R+100)an∣0.005
Compute
Compute
The equation gives 294.46 months, so payoff occurs in month 295 and eliminates 65 scheduled months.
n=294.462978,npayoff=⌈n⌉=295
Answer
Answer
The mortgage term is shortened by 65 months, which is choice C.
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