Compound interest is the interest that is calculated on the initial principal and also on the accumulated interest of previous periods of a loan or deposit. It is the interest that is calculated more than once in a year, or the interest that is calculated on the principal amount and the interest earned in the previous periods.

Formula for compound interest:

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

where,

A = Compound Interest

P = Principal Amount

r = Rate of Interest

n = Number of times the interest is compounded in a year

t = Number of years

For the given question,

A = 4P

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

4P = P(1 + r/n)^ (nt)

(1 + r/n)^ (nt) = 4

We need to find the value of ‘t’, i.e., the number of years for which the sum of money four folds itself.

We are given that the sum four folds itself in 24 years.

We need to find the number of years for which it sixteen folds itself.

Let us assume that the time required for the same to sixteen fold itself is ‘t’ years.

We have,

(1 + r/n)^ (nt) = 16

We know that the time taken for the sum of money to four fold itself is 24 years.

Therefore,

(1 + r/n)^ (24n) = 4

(1 + r/n)^ (nt) = 16

We need to find the value of ‘t’.

(1 + r/n)^ (24n) = 4

(1 + r/n)^ (nt) = 16

Dividing,

(1 + r/n)^ (nt)/(1 + r/n)^ (24n) = 16/4

(1 + r/n)^ (nt – 24n) = 4

Taking ‘nth’ root on both sides,

(1 + r/n)^ (t – 24) = 4^1/n

t – 24 = log4^1/n (1 + r/n)

t = 24 + log4^1/n (1 + r/n)

Therefore, the time taken for the sum of money to sixteen fold itself is 48 years.

Hence, the correct answer is Option B: 48 years.

If you think the solution is wrong then please provide your own solution below in the comments section .