Original practice · fully worked
Original variant: six-year balance gap between crediting methods
A reserve places 2,000 in each of two accounts. Account S earns 6% annual simple interest. Account M earns a 4.8% nominal annual rate convertible monthly. No withdrawals occur. Determine the absolute difference between the two balances after six years.
- A
4.70 - B
28.36 - C
54.02 - D
120.00 - E
185.98
Answer and calculation
The simple-interest balance is 2,720.00 and the monthly compound balance is 2,665.98, giving an absolute difference of 54.02, choice C.
Setup
Setup
Compute each six-year balance under its own crediting rule.
AS=2000(1+0.06(6)) Model
Model
The monthly rate is 0.4%, and six years contain 72 monthly periods.
AM=2000(1+0.048/12)72 Compute
Compute
The two balances are 2,720.00 and 2,665.9826.
AS=2720.00 AM=2665.9826 ∣AS−AM∣=54.0174 Answer
Answer
The absolute balance gap is approximately 54.02, which is choice C.
∣AS−AM∣≈54.02(C) 