Michael has been offered the following investment opportunity.

Question

He promises to invest 10000 dollars now and 37703.5 dollars in two years, and in return will receive 33650 dollars in one year and 14067.54 dollars in three years. What are the possible effective rates of interest?

Answer 1

Let r be the effective annual interest rate and let v = 1 / 1 + r

Now, the cash flow timeline would be:

1. t = 0 : -10,000 --> the investment that Michael had made now
2. t = 1 : +33,650 --> the money he will receive in 1 year
3. t = 2 : -37,703.50 --> the money he invests in 2 years
4. t = 3 : +14,067.54 --> the money he will receive in 3 years

So after knowing the timeline, the net present value equation will be:

-10,000 + 33,650v - 37,703.5v² + 14,067.54v³ = 0

This cubic equation yields 2 positive solutions for r. By testing values (or using numerical moethods), the solutions are approximately: r ≈ 0.10 and r ≈ 0.20.

So that means that the possible effective rates of interest are approximately 10% and 20%.