Reading 6-Time value of money


Can someone please explain why the compounded semiannually interest rate should be converted to EAR below? And as per my calculation, the answer should be $528,150 (calculator on BEG mode for 4 yrs) but the correct answer is $549,487.

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?

A) $528,150
B) $549,487
C) $574,253.

Thanks very much.

The question is slightly ambiguous; it should have specified that the 4% rate is nominal.

In any case, you don’t have to convert it to an EAR; you can use 2% semiannually for 8 semiannual periods.

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To calculate the PV of the payments at time 4, it’s better to use the EAR of 4.04% to match the annual payment frequency. The PV is 25,000 * 1.0404/0.0404 = 643,811.88.

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thanks millions!!