Question

Today (t=0) your daughter is born and you decide to start saving for her education. You figure that you will need to pay for 5 years of undergraduate engineering at $20,000 per year (from t=18 through t=22), and two years for graduate school at $30,000 per year (t=23 and t=24). you decide to start your equal-sum deposits on her 5th birthday. You plan to make equal-sum deposits all the way through to her 24th birthday (so including t=5, including t=10, and including t=24). How much do the annual deposits need to be in this case?

Answer 1

(Note: As interest rate is not given, it is assumed as 5% per annum.)

t	Year	Cash Flow	Discounting Factor [1/(1.05^year)]	PV (cash flow*discounting factor)
5	1		0.952380952	0
6	2		0.907029478	0
7	3		0.863837599	0
8	4		0.822702475	0
9	5		0.783526166	0
10	6		0.746215397	0
11	7		0.71068133	0
12	8		0.676839362	0
13	9		0.644608916	0
14	10		0.613913254	0
15	11		0.584679289	0
16	12		0.556837418	0
17	13		0.530321351	0
18	14	20000	0.505067953	10101.35906
19	15	20000	0.481017098	9620.341962
20	16	20000	0.458111522	9162.23044
21	17	20000	0.436296688	8725.933752
22	18	20000	0.415520655	8310.413097
23	19	30000	0.395733957	11872.01871
24	20	30000	0.376889483	11306.68449
			PV = (sum of PVs)	69098.98151

Amount reqiured to be deposited = Equal Annual Instalments for 20 years

= P*i*(1+i)^n/[(1+i)^n-1]

where,

P = Principal = 69099

i = interest rate = 0.05

n = no of periods = 20

Therefore, Equal Annual Instalment = 69099*0.05*(1+0.05)²⁰/[(1+0.05)²⁰-1] = 9167.0109/1.6533 = $5544.67

(Note: If we ignore the interest rate(although it is not a REALISTIC assumption), the answer would be [{(20000*5)+(30000*2)}/20] = 8000)

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