Answer:

To find the time it takes for Rs. 1500 to amount to Rs. 2160 at an annual compound interest rate of 20%, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

where:

A = the final amount (Rs. 2160)

P = the principal amount (Rs. 1500)

r = the annual interest rate (20% or 0.20 as a decimal)

n = the number of times interest is compounded per year (annually, so n = 1)

t = the time in years (unknown, what we want to find)

Plugging in the values we have:

2160 = 1500 * (1 + 0.20/1)^(1*t)

Now, let's solve for t:

Divide both sides by 1500:

2160/1500 = (1.20)^t

Simplify:

1.44 = 1.20^t

To solve for t, take the logarithm of both sides. Let's use the natural logarithm (ln):

ln(1.44) = ln(1.20^t)

Since ln(1.20^t) can be simplified to t * ln(1.20), divide both sides by ln(1.20):

t = ln(1.44) / ln(1.20)

Using a calculator, we get:

t ≈ 0.33 years

So, it takes approximately 0.33 years (or about 4 months) for Rs. 1500 to amount to Rs. 2160 at a 20% annual compound interest rate.

Explanation:

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Verified answer

Answer:

The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

where A is the amount, P is the principal, r is the rate of interest per annum, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have:

P = Rs. 1500

A = Rs. 2160

r = 20%

n = 1 (compounded annually)

Substituting these values into the formula gives:

2160 = 1500(1 + 0.2/1)^(1t)

Simplifying this equation gives:

(1.44)^t = 2160/1500

Taking logarithms of both sides gives:

t log(1.44) = log(2160/1500)

Solving for t gives:

t = log(2160/1500)/log(1.44) ≈ **3 years** .

Therefore, it will take approximately 3 years for Rs. 1500 to amount to Rs. 2160 at a rate of 20% per annum compounded annually.