Consider establishing a college funds at a bank for a couple with a 5-year old c

Question

Consider establishing a college funds at a bank for a couple with a 5-year old child. The college funds will earn 8% interest (market rate), compounded quarterly. Assuming that the child enters college at age 18, the couple estimate that an amount of $30,000 per year, in terms of today’s dollars, will be required to support the child’s college expenses for 4 years. The college expense is estimated to increase at an annual rate of 6% due to inflation.
Determine the equal quarterly deposits the couple must make until they send their child to college. Assume that the first deposit will be made at the end of the first quarter after the child’s 5th birthday and deposits will continue until the child reaches age 17. The child will enter college at age 18 and the annual college expense will be paid at the beginning of each college year. In other words, the first withdrawal will be made at age 18.

Explanation / Answer

Very interesting problem!!!! I did this in following way :- 1. First Calculated the Child's Fee reqd at Begining of 18,19,20 & 21 Yrs by taking $30000 at Y18 & increasing it by 6% every year. That gives the Fee to paid at T18,t19,T20 & t21. 2. At Y18, fee is $30,000 Y19 will be 30000*(1+6%) = 31,800, Y20=31800*(1+6%)= 33708, Y21=33708*(1+6%)=35730. PV of Fee at Y18=30000, at Y19=31800/(1+8%)^1=29,444, at Y20=33708/(1+8%)^2=28899, at Y21=35730/(1+8%)^3=28364. Sp PV of Corpus reqd at Start of Y18 = 30000+29444+28899+28364 = 116,708 3. There is a trick here. The COntribution stop at end of 16 Yrs when child turns 17. But Fee payment start at when child turns 18. So the Corpus at Start of Y17 earns interest at 8% for 1Yr till child turns 18. So The corpus at Start of Y17 = PV of Y18/(1+8%) = 116,708/(1.08) = $108,063 4. Now from Y5 to Y17. From Y5-Y17, it is Ordinary Annuity as payment are at end of QUarter. So the FV of amount needed from Y5-Y17 is PV of Fee = $108,063 5. Recall that from Y5-Y17 (ie n=4qtr/yr*12yrs = 12*4=48 period) is Ordinary annuity & is given by FVAn= PMT*[(1+i)^n - 1]/i. So we have here i=8% & FVAn = $108,063 . Solving for PMT, we get PMT = 108,063/{[(1+8%/4)^48 - 1]/(8%/4)} = 1361.79 So Couple needs to make Quarterly contribution of $1361.79 from Y5-Y17.

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