To calculate the amount that needs to be invested every year to accumulate a sum of ₹300,000 at the end of 10 years with an annual interest rate of 10% (compounded annually), we can use the formula for the Future Value of an Annuity:

$\text{Future Value} = \text{Investment} \times \frac{(1 + r)^n - 1}{r}$

Where:

• Future Value (FV) is ₹300,000.
• Investment (PMT) is the annual investment we need to find.
• r is the annual interest rate (10% or 0.10).
• n is the number of years (10 years).

We rearrange the formula to solve for the annual investment (PMT):

$PMT = \frac{FV \times r}{(1 + r)^n - 1}$

Substituting the values:

$PMT = \frac{300,000 \times 0.10}{(1 + 0.10)^{10} - 1}$

$PMT = \frac{30,000}{(1.10)^{10} - 1}$

Let's calculate the exact value.The amount that needs to be invested every year is approximately ₹18,824 to accumulate ₹300,000 at the end of 10 years, with an interest rate of 10% compounded annually.

Would you like further details or have any questions?

Here are five related questions that might interest you:

1. How does the investment amount change if the interest rate increases to 12%?
2. What would be the required annual investment for a 5-year period instead of 10 years?
3. How much would you accumulate if you invested ₹20,000 annually at the same rate and duration?
4. What is the formula for calculating the future value with different compounding frequencies (e.g., semi-annually)?
5. How does the formula change if the interest is compounded monthly instead of annually?

Tip: Understanding the impact of compounding can significantly help in planning long-term investments. The frequency of compounding plays a critical role in the growth of your investment.