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.