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

To solve this problem, we will 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

Given in the problem: A = Rs. 68921 P = Rs. 64000 r = 5% per annum = 0.05 (in decimal) n = 2 (since the interest is compounded half yearly)

We need to find t.

Substituting the given values into the formula, we get:

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

Solving the equation for t:

(1 + 0.05/2)^(2t) = 68921 / 64000 (1.025)^(2t) = 1.076828125

Taking the natural logarithm (ln) on both sides:

2t * ln(1.025) = ln(1.076828125) 2t = ln(1.076828125) / ln(1.025)

Calculating the values:

2t = 0.075 / 0.024692612590372152 t = 0.075 / (2 * 0.024692612590372152) t = 1.52 years (approximately)

So, it will take approximately 1.52 years for Rs. 64,000 to amount to Rs. 68921 at 5% per annum interest being compounded half yearly.