A sum of Rs. 12,000, deposited at compound interest becomes double after 5 years. How much will it be after 20 years?a)Rs. 1,44,000b)Rs. 1,20,000c)Rs. 1,50,000d)Rs. 1,92,000Correct answer is option 'D'. Can you explain this answer?

Question

Answer

D

Answer

Given:

Amount deposited = Rs. 12,000
Time period = 5 years

To find:

Amount after 20 years

Solution:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years

In this case, the amount becomes double after 5 years. Therefore, the final amount (A) after 5 years will be Rs. 24,000.

Rs. 24,000 = Rs. 12,000(1 + r/n)^(n*5)

Now, we need to find the value of r/n to calculate the amount after 20 years.

Let's solve for r/n:
24000/12000 = (1 + r/n)^(5)
2 = (1 + r/n)^(5)

Taking the fifth root of both sides:
(1 + r/n) = 2^(1/5)
(1 + r/n) ≈ 1.1487

Now, let's substitute this value in the formula to find the amount after 20 years:

A = Rs. 12,000(1 + 1.1487)^(5*4)
A = Rs. 12,000(1.1487)^20
A ≈ Rs. 1,92,000

Therefore, the amount will be approximately Rs. 1,92,000 after 20 years. Hence, option D is the correct answer.

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