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

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 = $4,56,976 P =$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.