A sum of ₹20,000 is invested at a compound interest rate of 10% per annum, compounded annually. How many years will it take for the investment to grow to ₹50,000?5 years7 years10 years11 years

To solve this problem, we can 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 = the time the money is invested for in years

We know that A = ₹50,000, P = ₹20,000, r = 10% or 0.10 (in decimal), and n = 1 (since it's compounded annually). We need to find t.

So, we can set up the equation as follows:

50,000 = 20,000 (1 + 0.10/1)^(1*t)

Solving for t, we get:

(50,000 / 20,000) = (1 + 0.10)^t

2.5 = 1.10^t

Taking the natural logarithm (ln) of both sides to solve for t, we get:

ln(2.5) = t * ln(1.10)

t = ln(2.5) / ln(1.10)

Calculating the above expression, we get t approximately equal to 9.6 years.

However, since we can't have a fraction of a year in this context, we'll need to round up to the nearest whole number, which gives us 10 years.

So, it will take 10 years for the investment to grow to ₹50,000.