- A sum of money doubles itself in 10 years. A compound interest is charged on it at x% p.a. With the same rate p.a. it will four fold itself in
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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