# Discount how many years?

Saw this one a wehile ago and a bit confused:

Investor sets up fund to pay 10,000 in perpetuity. The first payment is made exactly 4 years from today. The initial money is deposited immediately and earns 4%, compounded semi annually. How much money must the investor donate today as a full and final payment?

Easy right? Find the annually compounded interest rate (1.0404), then the final value of the perpetuity (10,000/0.0404 = 247,525). This then needs to be discounted back to the present day. Deposit immediately (n=0) and pay at the start of 4th year (n=4) so value must be 247,525/1.0404^4 = 211,260.

WRONG (apparently)

The answer said that n should be 3 so the end value is 219,795. I don’t get this at all! Exactly 4 years from the deposit date means 4 years of annual compounding right? I don’t like to suggest that an answer is wrong, as I imagine CFA people are writing them, so am I making a mistake somewhere?

The formula 10,000 / .0404 is used when the first payment is made one year from today. We need to move our valuation date up 3 years so that the first payment is made on day 1 of year 4.

Or if you wanted to discount 4 years you could’ve used the immediate version and done 10,000 + 10,000/.0404 and then discounted that back 4 years.

Thanks!