AuthorTopic: tvm (annuity) question
Gignac
@2013-06-29 14:22:25
If the expected tuition expense for the eldest child is \$160,000 for college tuition and college begins 7 years, with an expected return of 8%, how much would have to be invested to have \$40,000 at the beginning of each year starting in seven years? Any help would be great.
meatball
@2013-07-17 22:03:40
This is a two-part problem. First you need the PV of the tuition payments at t=7. Using the TI you set Pymt = 40,000, Int = 8%, n = 4 and set it to annuity due. Then calc the PV, which is \$143,083.88.

That is the PV at t=7. To determine the lump sum today (at least that sounds like what its asking) do FV = 143,083.88 N = 7 and Int = 8% (don't forget to put the calculator back to end mode). Calc the PV, which equals 83,488.07

thesun
@2014-08-08 23:54:57
Here's my solution:

(1) First, determine how much money you will need when your eldest child starts college. Let's call that Year 0. If the tuition is to be paid at the beginning of each year for 4 years, then this is an annuity due with 4 payments of \$40,000 at an interest rate of 8%.

This can be expressed as: (\$40,000)(P/A, I=8%, N=4) = (\$40,000)[(1-(1.08)^-4)/0.08] (I got this formula from a finance textbook or just punch the numbers into your BAIIPlus or TI financial calculator). = \$132,485.07.

This, however, is not the correct answer because the formula above assumes payments are made/received at the END of the year. Thus, to get the annuity due numbers, we just multiply by 1.08: \$132,485.07*1.08 = \$143,083.87.

(2) Now, since your eldest child doesn't begin college for 7 years, we can accrue compounded interest during that time. Therefore, we can just discount the amount needed in Year 0 to determine how much we have to invest today (Year "-7"): \$143,083.87/(1.08)^7 = \$83,488.07

Let's check to see if this answer is correct:

(1) Invest \$83,488.07 today at 8% interest for 7 years.

(2) Seven years from now (Year 0) we will have (\$83,488.07)(1.08)^7 = \$143,083.87.

(3) We will pay \$40,000 immediately so we are left with \$143,083.87 - \$40,000 = \$103,083.87.

(4) This compounds for a year at 8% so will have in Year 1: (\$103,083.87)(1.08) = \$111,330.59 and then we pay out 40,000 again to get \$71,330.59.

(5) Right after paying tuition in Year 2 we will have (\$71,330.59)(1.08) - \$40,000 = \$37,037.04

(6) And at the beginning of Year 3 we will have (\$37,037.05)(1.08) - \$40,000 = ZERO!

Thus to pay for a \$40,000 college tuition due at the beginning of each year for four years starting seven years from now, we need to invest \$83,488.07 today.

(P.S. I don't think even Haaaaaaarvard charges that much, at least not yet!)

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