If a sum of ₹10,000 is to be deposited in equal installments in 5 years at the rate of 24% p.a. Find amount deposited in each installment?


To determine the equal installments required to deposit ₹10,000 over 5 years with an interest rate of 24% per annum, we can use the formula for the **Future Value of an Annuity (FVA)**.

The formula is:

\[
FVA = \frac{P \times \left( (1 + r)^n - 1 \right)}{r}
\]

Where:
- \( FVA \) = Future Value of the Annuity (₹10,000)
- \( P \) = Amount of each installment (unknown)
- \( r \) = Interest rate per period (24% annually or 0.24)
- \( n \) = Number of periods (5 years)

Rearranging to solve for \( P \):

\[
P = \frac{FVA \times r}{\left( (1 + r)^n - 1 \right)}
\]

Substituting the given values:

\[
P = \frac{10,000 \times 0.24}{\left( (1 + 0.24)^5 - 1 \right)}
\]

First, calculate \((1 + 0.24)^5\):

\[
(1.24)^5 = 2.9297
\]

Then:

\[
P = \frac{10,000 \times 0.24}{2.9297 - 1}
\]

\[
P = \frac{2,400}{1.9297} \approx 1,243.68
\]

Thus, the amount to be deposited in each installment is approximately ₹1,243.68.

Would you like more details on the steps or the concepts involved? 

Here are 5 related questions to deepen your understanding:
1. How would the installment change if the interest rate were 18% instead of 24%?
2. What would happen to the installment amount if the time period was reduced to 3 years?
3. How does compound interest affect installment amounts compared to simple interest?
4. What is the total amount deposited over 5 years in this scenario?
5. How does the number of periods affect the future value of an annuity?

**Tip:** When dealing with annuities, the interest rate significantly impacts the installment size, so small changes in the rate can lead to large differences in payments.

If a sum of ₹10,000 is to be deposited in equal installments in 5 years at the rate of 24% p.a., find the amount deposited in each installment.

Learn how to calculate the equal installment required to deposit ₹10,000 over 5 years with an interest rate of 24% per annum. This problem involves financial mathematics, including the Future Value of an Annuity formula. Suitable for students in Grades 11-12 or finance undergraduates.

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