Question

Saving for College: A Mini Case Your life is changing rapidly. You are still in your first semester of the MBA program at Cal Poly, and you have met some very nice people. But there are big changes on the horizon-your significant other is pregnant and the baby is due around the first week of July, 2019! Of course your little pride-and-joy is going to be cute AND smart. After much consultation, your significant other and you have decided that you want to send the little one to a private college (when the time comes). Private colleges are very expensive. A recent survey estimates the current cost to be around $37,820 for one year. This costs covers tuition, fees, room, and board, and is based on an elite, private, four-year school in the Northeast of the United States. The cost is for the 2018-2019 school year. You expect these costs to increase by 3.9% per year over the foreseeable future (approximately the same rate as inflation.) Your child will most likely begin school eighteen (18) years after birth. Schools tend to demand payments upfront. Assume the cost of the whole first year tuition is due in July 2037. The whole second year tuition is due in July 2038, etc. You expect to invest your money in a manner that returns 7.50% per year over the foreseeable future. You want to start saving soon. In fact, you plan to invest money every year. To be precise, you will put away money once a year, every July starting when the baby is born, and ending in July, 2036 A. Suppose you want to save the same amount each year (in nominal dollars). How much will you have to save so that there is enough money to send your child to college? B. In the first part of this problem, you calculated the nominal amount saved each year. Of course, in real terms, the value of these amounts gets less and less over time due to inflation. Suppose you want to save the same real amount each year. How much will you have to save so that there is enough money to send your child to college? Please write down how much you will save each year in real dollars. Also provide the actual payments (in nominal dollars) made each year

Answer 1

Statement showing caculation of amount required in 2037
Particulars	Notes	$
Amount required for study as per servey of 2018-19(in $)	1	37820
Inflation rate per year	2	3.90%
Year(Time period after which money reuired)	3	18
cummulative inflation impact	4	1.9910
Amount required for study in 2037 (in $)(1*4)	5	75,301
Computation of savings per year
Interest rate	6	7.50%
Year(Time period after which money reuired)	7	18
present value factor for year1	8	0.9302
sum of present value factor (from year 1 to year 18)	9	9.7060
(sum of pvf=1/(1+.075)^n)
Solution A
Amount required to save for getting required amount in 2037		7,758
(75301/9.7060) i.e.(5/9)

Solution B
Statement showing calculation of Real Amount Saving
Year	Saving(As per Solution A)	Inflation Index	Real Amount	Inflation Amount	Total Nominal Payment
1	7,758	0.9625	7,466.99	291.21	7,758.20
2	7,758	0.9263	7,186.71	571.49	7,758.20
3	7,758	0.8916	6,916.95	841.26	7,758.20
4	7,758	0.8581	6,657.31	1,100.89	7,758.20
5	7,758	0.8259	6,407.42	1,350.78	7,758.20
6	7,758	0.7949	6,166.91	1,591.29	7,758.20
7	7,758	0.7651	5,935.43	1,822.77	7,758.20
8	7,758	0.7363	5,712.64	2,045.56	7,758.20
9	7,758	0.7087	5,498.21	2,259.99	7,758.20
10	7,758	0.6821	5,291.83	2,466.38	7,758.20
11	7,758	0.6565	5,093.19	2,665.01	7,758.20
12	7,758	0.6318	4,902.01	2,856.19	7,758.20
13	7,758	0.6081	4,718.01	3,040.19	7,758.20
14	7,758	0.5853	4,540.92	3,217.29	7,758.20
15	7,758	0.5633	4,370.47	3,387.73	7,758.20
16	7,758	0.5422	4,206.42	3,551.79	7,758.20
17	7,758	0.5218	4,048.52	3,709.68	7,758.20
18	7,758	0.5023	3,896.56	3,861.64	7,758.20
Total	139,648		99,016	40,631	139,648