In what time will Rs. 64,000 amount to Rs.68921 at 5% per annum interest being compounded half yearly?

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. 68921 P = Rs. 64000 r = 5% per annum = 0.05 (in decimal) n = compounded half yearly, so n = 2

We need to find t.

Substitute the given values into the formula:

68921 = 64000 (1 + 0.05/2)^(2t)

Simplify the equation to solve for t:

(68921/64000) = (1 + 0.025)^(2t)

1.076890625 = (1.025)^(2t)

Take the natural logarithm (ln) on both sides:

ln(1.076890625) = 2t * ln(1.025)

Divide both sides by 2*ln(1.025) to solve for t:

t = ln(1.076890625) / (2*ln(1.025))

Calculate the values:

t ≈ 1.5 years

So, Rs. 64,000 will amount to Rs.68921 at 5% per annum interest being compounded half yearly in approximately 1.5 years.