CFA Video: Effective Annual Rate and Annuity Example

John’s father will retire in 10 years. John plans to pay his father $30k annually starting 10 years from now. Assume he is able to invest at 5%, compounded semi-annually, how much should he invest today to meet his plan?

Answer:

This question tests the concept of effective annual rate (EAR), your understanding of annuity and net present value.

Since the interest is compounded semiannually, therefore, we need to find the EAR in order to simplify the calculations. By definition,

EAR = (1+5%/2)^2 – 1 = 5.0625%

Then we can find the NPV at t=9 by using the annuity equation. Note that this equation discounts the cash flows to t=9 NOT t=10,

NPV(t=9) = 30k/0.050625 = 593k

Finally we have to discount it to today’s present value, so he has to invest

593k/ (1.050625)^9 = 380k