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
Answer and calculation
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.
360−295=65 months(C) Calculator reproduction
BA II Plus keystrokes
- 2nd CLR TVM; 360 N; 0.5 I/Y; 200000 +/- PV; 0 FV; CPT PMT1199.10Scheduled payment.
- 1299.10 PMT; CPT N294.46Round up to the payoff month, then subtract from 360.
