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?
(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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