Question

In how many years will Rs.8000 amount to Rs. 9261 at 5% p.a. compounded annually?​

Answer 1

Answer:

After 3 years rupees 8000 will amount to 9261.

Step-by-step explanation:

Amount = 9261

Rate of interest = 5%

Principal = 8000

Formula for amount:

Where, P is principal, r is rate of interest and t is time in years.

On comparing both the sides.

Step-by-step explanation:

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Answer 2

In 3 years Rs. 8000 will amount to Rs. 9261 at 5% p.a. compounded annually.

Given : Rs.8000 amount to Rs. 9261 at 5% p.a. compounded annually

To find : The required number of years.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the required number of years)

Here, we will be using the following mathematical formula.

$A = P \: \times \: {(1 + \frac{r}{100} )}^{n}$

Where,

• A = Total amount after 'n' number of years
• P = Principal amount
• r = rate of interest per annum
• n = number of years

In this case,

• A = Rs. 9261
• P = Rs. 8000
• r = 5%
• n = ? (unknown quantity)

By putting the available data in the above mentioned mathematical formula we get :

$9261 = 8000 \times {(1 + \frac{5}{100}) }^{n}$

$\frac{9261}{8000} = {( \frac{1 \times 100 + 5}{100} )}^{n}$

$\frac{9261}{8000} = {( \frac{105}{100} )}^{n}$

${( \frac{21}{20}) }^{3} = {( \frac{21}{20} )}^{n}$

Which implies,

n = 3

So, required number of years = 3

Hence, in 3 years Rs. 8000 will amount to Rs. 9261 at 5% p.a. compounded annually.