Why should we convert the compounded semiannually interest rate to EAR below? It was not the case in any other questions. For example, if interest was compounded quarterly at 8%, I/Y would be 2 {8/4=2}. We do not calculate EAR.
Q: A successful investor has decided to set up a scholarship fund for deserving students at her alma mater. Her plan is for the fund to be capable of awarding $25,000 annually in perpetuity. The first scholarship is to be awarded and paid out exactly four years from today. The funds will be deposited into an account immediately and will grow at a rate of 4%, compounded semiannually, for the foreseeable future. How much money must the investor donate today to fund the scholarship?
As an aside, there is a way to use the 4% semi-annual rate, but it is far easier to use annual compounding of 4.04% to match the annual payment frequency. Plus it’s a little out of the LI syllabus scope.
Payment is annual, but interest rate is compounded semi-annually: you need an annual effective rate to match the payment frequency!!! That rate is 4.04%!!
PV at time = 25,000/0.0404 = 618,811.88
P/Y=1 C/Y=2 in order to use 4%
2ND CLR TVM
3 N 4 I 618,811.88 FV CPT PV -549,487.24
OR
CF worksheet
0 CF0 0 C01 3 F01 25000 C02 1000 ( just a large number of years) F02
2ND QUIT
NPV 4.04 (annual CF, so we need an EFFECTIVE ANNUAL rate) I CPT NPV 549,487.24
