At what rate of interest per annum will Rs. 3000 amount to Rs. 3630 in 2 years, if the interest is compounded annually? Options 5% 12% 11% 10%
Question
At what rate of interest per annum will Rs. 3000 amount to Rs. 3630 in 2 years, if the interest is compounded annually?
Options:
- 5%
- 12%
- 11%
- 10%
Solution
To solve this problem, we need to use the formula for compound interest which is:
A = P (1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
Given in the problem: A = Rs. 3630 P = Rs. 3000 n = 1 (since the interest is compounded annually) t = 2 years
We need to find r.
Substituting the given values into the formula, we get:
3630 = 3000 (1 + r/1)^(1*2)
Solving the equation for r:
(3630/3000) = (1 + r)^2
1.21 = (1 + r)^2
Taking the square root of both sides:
1.1 = 1 + r
Subtracting 1 from both sides:
r = 0.1
Converting r to a percentage gives us the annual interest rate:
r = 0.1 * 100 = 10%
So, the annual interest rate is 10%.
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