Question

How long will it take to double a capital attracting interest at 6% com- pounded daily?

Answer 1

11.58 years

Explanation:

Given:

Interest rate = 6% compounded daily

daily interest =
`\frac{\textup{6}}{\textup{365}}` = 0.0164%

Let the capital amount be 'x'

hence, we have

2x = x (1 + r )ⁿ

here,

r is the rate of interest

n is the number of years

thus,

2 = ( 1 + 0.000164 )ⁿ

taking log both sides we get

㏒ 2 = n × ㏒ ( 1.000164 )

or

0.30103 = n × 7.1218 × 10⁻⁵

or

n = 4226.85 days

or

n =
`\frac{\textup{4226.85}}{\textup{365}}`

or

n = 11.58 years