Question

A sum of 12,000 deposited at compound interest becomes double after 5 years. After 20 years, it will become​

Answer 1

Answer:

The amount 12,000 doubles which means it becomes 2×12,000=24,000 after 5 years. This means that when the principal amount is Rs.12,000 and the time period is 5 years, the final amount will be Rs. 24,000. So from this we can calculate the interest rate by using the below formula. With the obtained interest rate, the principal amount Rs.12,000 and the time period 20 years, find the final amount at the end of 20th year.

Compound interest A is calculated by

=) A=P(1+R/100)T , where P is the

principal amount, T is the time period and R is the interest rate.

Complete step-by-step answer:

We are given that a sum of Rs.12,000 deposited at compound interest doubles after 5 years.

Twice or double of Rs. 12,000 is 2×12,000=Rs.24,000 .

So here Principal amount P is Rs.12,000, Time period T is 5 years and the final amount A is Rs.24,000.

Interest rate will be,

A=P(1+R/100)^T

⇒24,000=12,000(1+R/100)^5

⇒(1+R/100)^5=24,000/12,000=2

⇒(1+R/100)=

$\sqrt[5]{2} = equation1$

The above obtained equation is enough to find the amount after 20 years.

Therefore, the total amount after 20 years will be

A=P(1+R/100)^T

⇒A=12,000(1+R/100)20

We already know from equation 1 that (1+R/100)=

$a = 12000 (\sqrt[5]{2} {})^{20}$

$(1 + \frac{r}{100} ) = \sqrt[5]{2}$

Substituting this in the above equation, we get

$a = 12000( \sqrt[5]{2}) {}^{2}$

∴A=12,000×16=Rs.1,92,000

The amount after 20 years will be Rs. 1,92,000.

So, the correct answer is “Rs. 1,92,000”