Compound interest is the interest that is calculated on the initial principal amount and also on the accumulated interest of previous periods of a deposit or loan.
Compound Interest Formula:

Compound Interest (C.I) = P (1 + r/100) n - P
Where,
P = Principal Amount
r = Rate of interest per annum
n = Number of years

Given:
Principal Amount (P) = Sum of money
Rate of Interest (r) = x% p.a.

Now, we have to find the number of years (n) in which the sum of money will four fold itself at the same rate of interest p.a.

We know that,
Amount (A) = P (1 + r/100) n

As, Amount (A) = 4P
⇒ 4P = P (1 + r/100) n
⇒ 4 = (1 + r/100) n

Now, we have to find n.

We know that,
A sum of money doubles itself in 10 years at the same rate of interest p.a.

It means,
2P = P (1 + r/100) 10
⇒ 2 = (1 + r/100) 10

We know that,
A sum of money four fold itself in 20 years at the same rate of interest p.a.

It means,
4P = P (1 + r/100) 20
⇒ 4 = (1 + r/100) 20

Now, divide equation (1) by equation (2)

⇒ (1 + r/100) n/ (1 + r/100) 10 = (1 + r/100) 20/2
⇒ (1 + r/100) (n - 10) = (1 + r/100) 10
⇒ n - 10 = 10
⇒ n = 20

Hence, the sum of money four fold itself in 20 years at the same rate of interest p.a.

Answer: Option C (20 years)

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