Question

You plan to be a doting grandparent for your three adorable yet unborn tots (you love to plan ahead). You plan on setting up a trust fund to pay for their undergraduate educations. The fund will be set up to pay each little one $260,000 for the first year of school, then increase at 4% per year through graduation. Assume the grandkids graduate after 4 years. The oldest tot begins school in 35 years; the second one starts three years later and the last little one starts two years after the second. You have set aside $100,000 thus far. You earn 6% on your investments. Next year’s salary is expected to be $180,000. What fraction of your salary must you set aside if you get raises of 2% per year to make your vision a reality? You start your savings based on income one year from now and you make your last payment on the first grandchild’s first day at college.

Answer 1

	0	1	2	3	4	5	6
	T	T	T	T	T	T	T
	35	36	37	38	39	40	41
Oldest Tot	260,000	270,400	281,216	292,465
2nd Tot			260,000	270,400	281,216	292,465
3rd Tot				260,000	270,400	281,216	292,465
Total Requirement	260,000	270,400	541,216	822,865	551,616	573,681	292,465
PV factor	1	1/1/(1+6%)^1	1/(1+6%)^2	1/(1+6%)^3	1/(1+6%)^4	1/(1+6%)^5	1/(1+6%)^6
PV factor	1	0.94339623	0.88999644	0.83961928	0.792094	0.747258	0.704961
PV of fund	260,000	255,094	481,680	690,893	436,932	428,688	206,176
Total Funds required at T 35	2,759,463
Already set aside	100,000
FV of this amount @ 6% after 35 years	100000*(1+6%)^35
FV of this amount @ 6% after 35 years	768,609
Balance corpus required	1,990,854
P = PMT x (((1 + r)^n-(1+g)^n)/(r-g))
Where:
P = the future value of an annuity stream	1,990,854
PMT = the dollar amount of each annuity payment	To Calculate
r = the effective interest rate (also known as the discount rate)	6.00%
n = the number of periods in which payments will be made	35
g= Growth rate	2%
1990854=	PMT * (((1 + 6%)^35-(1+2%)^35)/(6%-2%))
1990854=	PMT * 142.1549
Annual Payment required=	1990854/142.1549
Annual Payment required=	14,004.82