To break down the compounding interest on an investment of ₹10,000,000, let's go through the basic formula of compound interest:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ = the amount of money accumulated after n years, including interest.
• $P$ = the principal amount (initial investment).
• $r$ = annual interest rate (in decimal form).
• $n$ = number of times interest is compounded per year.
• $t$ = time the money is invested for, in years.

Let's break down this formula with an example. Suppose you want to know the final amount after a certain period with different compounding frequencies (annually, semi-annually, quarterly, etc.) at a specific interest rate.

Example Calculation

Let's consider:

• Principal ($P$) = ₹10,000,000
• Annual Interest Rate ($r$) = 10% or 0.10
• Compounding Frequency ($n$) = 12 times per year (monthly)
• Time ($t$) = 5 years

Now, substitute these values into the formula:

$A = 10,000,000 \left(1 + \frac{0.10}{12}\right)^{12 \times 5}$

Let's calculate this step-by-step:The amount accumulated after 5 years with monthly compounding at a 10% annual interest rate on an initial investment of ₹10,000,000 will be approximately ₹16,453,089.35.

Breakdown of Growth:

• Initial Investment (Principal): ₹10,000,000
• Interest Earned Over 5 Years: ₹16,453,089.35 - ₹10,000,000 = ₹6,453,089.35

This growth is due to the effect of compounding, where interest is earned on both the initial principal and accumulated interest over time.

Would you like to see more details on how the interest accumulates over each year, or do you have any specific questions?

Related Questions:

1. How does changing the compounding frequency affect the total amount?
2. What would the amount be with a different interest rate, e.g., 8% or 12%?
3. How does compounding annually compare to monthly in this scenario?
4. How does the amount change if the investment period is extended to 10 years?
5. What is the impact of doubling the principal amount on the final accumulation?

Tip: Compounding more frequently (e.g., monthly vs. annually) generally results in higher returns because interest is applied more often.