Page 47 - DMGT409Basic Financial Management

Basic Financial Management

Notes CV can also be calculated in the following ways:

No. of years com- Compound interest
Year Amount paid ` Future value `
pounded factor
(1) (2) (3) (4) (5) = (2) x (4)
1 5000 4 1.262 6,310
2 10,000 3 1.191 11,910
3 15,000 2 1.124 16,860
4 20,000 1 1.05 21,000
5 25,000 0 1.00 25,000
Total 81,080

Compound Value of Annuity (Even Cash Flows)

Illustration 11: Mr. Ram deposits ` 500 at the end of every year, for 6 years at 6 per cent interest.
Determine Ram’s money value at end of 6 years.
Solution:

FV = P (1+I) + P (1+I) + --------------P (1+I)+P
n-1
n-n
n-2
n 1 2 n-1
FV = 500(1+0.06) +500(1+0.06) +500(1+0.06) +500(1+0.06) +500(1+0.06) + 500(1+0.06)
2
1
5
3
4
0
6
= 500(1.338) + 500(1.262) + 500(1.19) + 500(1.124) + 500(1.060) + 500(1.00)
= 669 + 631 + 595.5 + 562 + 530 + 500 = ` 3487.5
By using table format,
Year Amount Paid ` No. of years compounded Compound interest factor Future value `
1 500 5 1.338 669.00
2 500 4 1.262 631.00
3 500 3 1.191 595.50
4 500 2 1.124 562.00
5 500 1 1.06 530.00
6 500 0 1.00 500.00
Total 3,487.50
Short-cut formula
⎡ (1 + I) – 1⎤
n
CV = P ⎢ ⎥
n
⎣ I ⎦
Where,
P = Fixed periodic cash fl ow.
I = Interest rate.

n = Duration of the amount.
n
(1 I+ ) − 1 = (FVIFA )
1 I.n
(FVIFA ) = Future value for interest factor annuity at ‘I’ interest and for ‘n’ years.
I.n
Illustration 12: Take the above example.
6
⎛ (1 0.06+ ) − 1⎞
CV = 500 ⎜ ⎟
6 ⎝ 0.06 ⎠

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