In what time will $3,90,625 amount to $4,56,976 at 4% compound interest? Ops: A. 4 years B. 1 year C. 3 years D. 2 years
Question
In what time will 4,56,976 at 4% compound interest? Ops: A. 4 years B. 1 year C. 3 years D. 2 years
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 = the 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 = 3,90,625 r = 4% or 0.04 (in decimal) n = 1 (since it's compounded annually)
We need to find t.
Substituting the given values into the formula, we get:
4,56,976 = 3,90,625 (1 + 0.04/1)^(1*t)
Solving the equation for t, we get:
(4,56,976 / 3,90,625) = (1 + 0.04)^t
1.17 = 1.04^t
Taking the natural logarithm (ln) of both sides to solve for t, we get:
ln(1.17) = t * ln(1.04)
t = ln(1.17) / ln(1.04)
t ≈ 3 years
So, the answer is C. 3 years.
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