Problem 1: Andrew deposits $20 into a fund today (t = 0) and $40 fifteen years later. Interest is credited at a nominal discount rate d compounded quarterly for the first ten years, and at a nominal interest rate of 6% compounded semi-annually thereafter.
The accumulated balance in the fund at the end of thirty years is $200. Calculate d. (Round your answer to the 0.01%.)
Problem 2: Frank makes deposits of $100 at time t = 0, and $X at time t = 3. The fund grows at a force of interest
δ(t) = δt = t2/100 (t > 0)
The amount of interest earned from (t = 3) to (t = 6) is also X.
Calculate X.
Problem 3: Jennifer can receive one of the following payment streams:
(1) $100 at time t = 0, then $200 at time t = n and then $300 at time t = 2n.
(2) $600 at time t = 10.
At an annual effective interest rate of i, the present values of these two streams are equal. Given that vn = 0.76, determine i.