At what rate of compound interest per annum will a sum of Rs.1200 become Rs.1348.32 in 2 years? (a) 6% (b) 6.5% (c) 7% (d) 7.5%
To solve this question, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount after interest (Rs.1348.32),
P is the principal amount (Rs.1200),
r is the annual interest rate (which we need to find),
n is the number of times the interest is compounded per year (assuming it's annually, so n = 1),
t is the time in years (2 years).
Given:
A = 1348.32,
P = 1200,
n = 1,
t = 2.
The formula simplifies to:
1348.32 = 1200(1 + r)^2
Now, divide both sides by 1200:
(1 + r)^2 = 1348.32 / 1200
(1 + r)^2 = 1.1236
Take the square root of both sides:
1 + r = √1.1236
1 + r = 1.06
Now, subtract 1 from both sides:
r = 1.06 - 1
r = 0.06
Convert to a percentage:
r = 6%
So, the rate of compound interest is 6% per annum.
Answer: (a) 6%
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