In what time will Rs. 64,000 amount to Rs.68921 at 5% per annum interest being compounded half yearly?1(1/2) years1(1/3) years2(1/2) years2(1/3) years

The formula for compound interest 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: 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.

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) of both sides:

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

Solving for t:

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

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. Therefore, the closest answer is 1(1/2) years.

The formula for compound interest 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: 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.

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) of both sides:

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

Solving for t:

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

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. Therefore, the closest answer is 1(1/2) years.

The formula for compound interest 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: 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.

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 log (ln) of both sides:

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

Solving for t:

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

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. Therefore, the closest answer is 1(1/2) years.

The formula for compound interest 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 = 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:

1.076828125 = (1 + 0.025)^(2t)

Take the natural logarithm (ln) on both sides:

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

Solve for t:

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

t ≈ 1.5 years

So, the closest answer is 1(1/2) years.