Question

if one invests rs 10000 in a bank at a rate of interest 8% per annum ,how long will it take to double the money by compound interest? here 1.08 power5 =1.47

Answer 1

Answer:

" In 9 years the amount will get doubled. "

Solution:

Let, the time of investment is T years.

Given,

Principal = Rs. 10000

Rate of interest = 8%

Also, interest is compounded annually and in T years, the amount will get doubled.

Then 2 * 10000 = 10000 * (1 + 8/100)ᵀ

or, (1 + 8/100)ᵀ = 2

or, (108/100)ᵀ = 2

or, (1.08)ᵀ = 2

Taking log to both sides, we get

T log(1.08) = log(2)

or, T = log(2) / log(1.08)

or, T ≈ 9

∴ in 9 years the amount will get doubled.

Answer 2

Answer:

In 9 years the amount will get doubled.

Step-by-step explanation:

In this question,

We have been given that

Principle = Rs. 10000

Rate of interest = 8%

To find Time at which the amount will get doubled

Let the time in amount will get doubled be T years.

$Amount\ =\ principle(1\ +\ \frac{Rate}{100})^{t}$

Then $2\times 10000\ =\ 10000\times (1\ +\ \frac{8}{100})$

or, $(1\ +\ \frac{8}{100})^{t}\ =\ 2$

or, $(\frac{108}{100})^{t}\ =\ 2$

or, $(1.08)^{t}\ =\ 2$

Taking log both the sides, we get

T log(1.08) = log(2)

or, T = $\frac{log(2)}{log(1.08)}$

or, T = 9 years (approximately)

∴ In 9 years the amount will get doubled.