Original practice · fully worked
Original variant: annual deposit required under separated interest reinvestment
At each of six year-beginnings, a reserve receives the same deposit D. Each deposited principal earns 7% annually, paid out at each year-end into a side account earning 2%; principal itself remains intact. Immediately after year 6 interest is credited, the combined accounts must total 70,000. Calculate D.
- A
7,912.24 - B
8,377.67 - C
8,843.09 - D
9,308.52 - E
9,773.95
Answer and calculation
Six retained deposits contribute 6D. Their annual 7% interest receipts form an increasing stream reinvested at 2%. The combined factor is 7.519992, giving D = 9,308.52, choice D.
Setup
Setup
The principal account contains six unchanged deposits at the terminal date.
Model
Model
Year k interest equals 0.07kD and is carried from year k to year 6 at 2%.
I6=0.07Dk=1∑6k(1.02)6−k Compute
Compute
The combined coefficient is 7.51999184, so the required deposit is 9308.52.
70000=D(7.5199918386) D=9308.52074074 Answer
Answer
Each annual deposit is 9,308.52, selecting choice D.
D≈9308.52(D) 