To calculate the total amount after 1 year with monthly compounding, we use the compound interest formula:

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

Where:

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

Given:

• Principal ($P$) = 50,00,000 INR
• Monthly interest rate = 10% = 0.10 (since it's monthly, no need to divide by 12)
• $n = 12$ (compounded monthly)
• $t = 1$ year

Now, let's plug in the values:

$A = 50,00,000 \times \left(1 + \frac{0.10}{12}\right)^{12 \times 1}$

I’ll calculate this for you.The total amount after 1 year, with a monthly compounded interest rate of 10%, will be approximately ₹55,23,565.34.

Would you like to explore any details or have any questions?

Here are 5 related questions to consider:

1. How would the total amount change if the interest rate was compounded quarterly instead of monthly?
2. What would be the difference if the interest rate was annually compounded?
3. How does changing the interest rate to 8% affect the total amount after 1 year?
4. What would the total amount be after 2 years with the same monthly compounding?
5. How much interest is earned specifically during the last month?

Tip: When dealing with compound interest, the frequency of compounding (monthly, quarterly, annually) can significantly impact the final amount.