At what percent annum will Rs. 3,000 amount to Rs. 3,993 in 3 years if the interest is compounded annually?A) 12%B) 15%C) 25%D) 10%
Question
At what percent annum will Rs. 3,000 amount to Rs. 3,993 in 3 years if the interest is compounded annually?A) 12%B) 15%C) 25%D) 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
In this case, we know that: A = Rs. 3,993 P = Rs. 3,000 n = 1 (since the interest is compounded annually) t = 3 years
We need to find r (the annual interest rate). So, we rearrange the formula to solve for r:
r = [(A/P)^(1/nt) - 1] * n
Substituting the known values:
r = [(3993/3000)^(1/(1*3)) - 1] * 1
r = [1.331^(1/3) - 1]
r = 0.1 or 10%
So, the annual interest rate that will make Rs. 3,000 amount to Rs. 3,993 in 3 years with annual compounding is 10%. Therefore, the answer is D) 10%.
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