Page 35 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Personal Financial Planning

Notes Short-cut formula
⎡ (1 + I) – 1⎤
n
CV = P
n ⎢ ⎥
⎣ I ⎦
Where,
P = Fixed periodic cash flow.
I = Interest rate.
n = Duration of the amount.

( + )1I n − 1
= (FVIFA )
1 I.n
(FVIFA ) = Future value for interest factor annuity at ‘I’ interest and for ‘n’ years.
I.n
Illustration 17
Take the above example.

⎛ (10.06+ ) − 1 ⎞
6
CV = 500 ⎜ ⎟
6 ⎝ 0.06 ⎠
= 500 [6.975] = ` 3487 = 50

Notes See the compound value of annuity table of one rate for 6 years at 6 per cent interest.

2.6.5 Compound Value of Annuity Due

Illustration 18
Suppose you deposit ` 2500 at the beginning of every year for 6 years in a saving bank account
at 6 per cent compound interest. What is your money value at the end of the 6 years?
Solution:
⎛ (10.06+ ) − 1 ⎞
6
CV = 2500 ⎜ ⎟ (1 + 0.06)
6 ⎝ 0.06 ⎠
= 2500 (6.975) (1 + 0.06) = ` 18,483.75
Through the Table format

Compound Compound
Year Cash outflow ` No. of times compounded
factor value (`)
1 2500 6 1.419 3,547.50
2 2500 5 1.338 3,345.00
3 2500 4 1.262 3,155.00
4 2500 3 1.191 2,977.50
5 2500 2 1.124 2,810.00
6 2500 1 1.06 2,650.00
T O T A L 18,485.00

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