Quant Methods Annuity

Suppose you plan to send your daughter to college in 3 years You expect her to earn 2/3 of her tuition payment in scholarship money, so you estimate that your payments will be $10 000 a year for 4 years. To estimate whether you have set aside enough money, you ignore possible inflation in tution payments and assume that you can earn 8 percent annually on your investments. How much should you set aside now to cover these payments?

I ended up getting an answer of $26 292.77. The answer is $28 396.15 It seems I have discounted one period too far. However I do not understand why they only discount the original figure backwards by 2 periods, not 3? (as you have to send your daughter to college in 3 years, not 2).

Any help would be fantastic. Thanks

Draw a timeline at first.

If you discount the $10,000 starting with year 3 for four years assuming your calculator in in END-Mode you get the PV of the payments at the beginning of year three ($33,121), which is equal to the PV at the end of year two.

Recall that the END-Mode assumes year and payments. Hence, for getting the PV at year 0 you only need to discount back by 2 years, not by 3. Alternatively you could change to BGN-Mode and discount 3 years. Although more time consuming the result will be the same ($ 28,396).

Regards, Oscar

What i cant tell is whether the father has to make the first payment at the end of 2nd year or end of 3rd year.
The question doesn’t say anything about when the first payment is to be made.