A sum of money lent put at 11% per annum amount to ₹ 4491 in 2years 3 months what it about to in 3 years

To find out how much the sum of money will amount to in 3 years at an interest rate of 11% per annum, we first need to understand the relationship between principal, interest rate, and time. In your case, we know the amount after 2 years and 3 months, which is ₹4491. Let's break this down step by step.

Step 1: Determine the Principal Amount

First, we need to calculate the principal amount (the original sum of money lent) using the formula for simple interest. The formula for the total amount A after time t at an interest rate r is given by:

A = P + I

where I (Interest) can be calculated as:

I = P * r * t

Here, A is the amount after the interest is added, P is the principal, r is the rate of interest per year (expressed as a decimal), and t is the time in years.

Step 2: Convert Time into Years

Since the time given is 2 years and 3 months, we convert this into years. 3 months is equal to 3/12 = 0.25 years. Therefore, the total time t is:

t = 2 + 0.25 = 2.25 years

Step 3: Calculate the Interest Earned

We know that the total amount after 2.25 years is ₹4491. Rearranging the total amount formula to find P, we have:

P = A / (1 + rt)

Substituting the known values:

P = 4491 / (1 + 0.11 * 2.25)

Calculating the interest part:

0.11 * 2.25 = 0.2475

So, we have:

P = 4491 / (1 + 0.2475) = 4491 / 1.2475

Now we calculate P:

P ≈ ₹3600

Step 4: Calculate the Amount After 3 Years

Now that we have the principal amount, we can find out how much this will amount to after 3 years. Using the same formula for total amount:

A = P(1 + rt)

For 3 years, substituting the values we have:

A = 3600(1 + 0.11 * 3)

Calculating the interest part:

0.11 * 3 = 0.33

So, we have:

A = 3600(1 + 0.33) = 3600 * 1.33

Finally, calculating A gives:

A ≈ ₹4788

Final Amount

Thus, the sum of money lent will amount to approximately ₹4788 after 3 years at an interest rate of 11% per annum. This calculation illustrates how interest accumulates over time, and it’s a useful way to understand how investments grow.