Page 48 - DMGT409Basic Financial Management

Unit 3: Time Value of Money

= 500 [6.975] = ` 3487 = 50 Notes

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

Compound Value of Annuity Due

Illustration 13: 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:

⎛ (1 0.06+ ) − 1⎞
6
CV = 2500 ⎜ ⎟ (1 + 0.06)
6 ⎝ 0.06 ⎠
= 2500 (6.975) (1 + 0.06) = ` 18,483.75
Through the Table format
Year Cash outfl ow ` No. of times compounded Compound factor Compound 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
Total 18,485.00

Doubling Period

Doubling period is the time required, to double the amount invested at a given rate of interest. For
example, if you deposit ` 10,000 at 6 per cent interest, and it takes 12 years to double the amount.
(see compound value for one rupee table at 6 per cent till you find the closest value to 2).

Doubling period can be computed by adopting two rules, namely:
1. Rule of 72: To get doubling period 72 is divided by interest rate.

Doubling period (D ) = 72 ÷ I
p
Where,
I = Interest rate.
D = Doubling period in years.
p
Illustration 14: If you deposit ` 500 today at 10 per cent rate of interest, in how many years will
this amount double?
Solution:
D = 72 ÷ I = 72 ÷ 10 = 7.2 years (approx.)
p
2. Rule of 69 : Rule of 72 may not give the exact doubling period, but rule of 69 gives a more
accurate doubling period. The formula to calculate the doubling period is:
D = 0.35 + 69 / I
p

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