A sum of `12,000.00 deposited at compound interest becomes double at the end of 5 years. At the end of 15 years the sum will be:

Correct option is D

Given:

Amount =12,000.00

compound interest becomes double = 5 years.

Solution:

Let the initial principal amount be P = 12000 .

It is given that the sum becomes double at the end of 5 years, so:

2P = $$P \times (1 + r)^5$$​​

Simplifying, we get:

2 = $$(1 + r)^5$$​​

Taking the 5th root of both sides:

1 + r = $$2^{1/5}$$​​

Now, to find the amount after 15 years, we use the compound interest formula:

A =$$P \times (1 + r)^{15}$$​​

Substituting the value of 1 + r as$$2^{1/5}$$​ , we get:

A = $$12000 \times (2^{1/5})^{15}$$​​

Simplifying the exponents:

A =$$12000 \times 2^3 = 12000 \times 8$$​ = 96000

Thus, the sum at the end of 15 years will be 96,000 .