Question

An investment in year 0 of $1,000 has returns of $5,000 in year 1, 4 and 5. The returns in years 2 and 3 are unknown. If the investment has a rate of return of 12%, the annual equivalent at 12% should be approximately

Answer 1

We have the following information

Year 0: Initial Cost ($)	1,000
Year 1: Returns ($)	5,000
Year 2: Returns ($)
Year 3: Returns ($)
Year 4: Returns ($)	5,000
Year 5: Returns ($)	5,000

Interest Rate (i) = 12% or 0.12

Assuming that like year 1, 4, and 5, returns in the year 2 and 3 are also equal to $5,000

Annual Equivalent Amount = – 1,000(A/P, 12%, 5) + 5,000

Annual Equivalent Amount = – 1,000[0.12(1 + 0.12)⁵/((1 + 0.12)⁵ – 1)] + 5,000

Annual Equivalent Amount = – (1,000 × 0.277) + 5,000

Annual Equivalent Amount = – 277.41 + 5,000

Approximate Annual Equivalent Amount = $4,722.59