Original practice · fully worked
Original variant: matching maintenance-account forces
A building reserve compounds at 6% effective annually. A separate account receives 2,000 at time 1 and earns simple interest at annual rate y. At time 5 the two accounts have equal instantaneous forces. Find the second account's value at time 5.
- A
2,400.00 - B
2,500.00 - C
2,607.82 - D
2,720.00 - E
2,800.00
Answer and calculation
Force equality gives y = 7.5977%, and four years of simple accumulation gives 2,607.82, choice C.
Setup
Setup
The simple-interest account has run for four years when the instantaneous rates are compared.
δ=ln(1.06),1+4yy=δ Model
Model
Equating its current force to the constant force of the compound account isolates y.
y=1−4δδ=0.0759774 Compute
Compute
The resulting simple rate is 0.0759774; inserting it in the four-year accumulation function gives 2,607.819.
A=2000(1+4y)=2607.819 Answer
Answer
The account value is therefore 2,607.82, choice C.
A=2607.82(C) 