Math Problem Statement

My capital is 50 lakhs. If I earn 10% interest every month, what will be my capital after 8 years if I compound every month

Solution

To calculate the future value of your capital when compounding monthly, we can use the formula for compound interest:

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

Where:

  • AA is the amount of money accumulated after nn years, including interest.
  • PP is the principal amount (initial capital), which is 50 lakhs (5,000,000).
  • rr is the annual interest rate (in decimal form). Since you're earning 10% monthly, the annual interest rate would be 10%×12=120%10\% \times 12 = 120\%, so r=1.20r = 1.20.
  • nn is the number of times that interest is compounded per year. Here, n=12n = 12 (monthly compounding).
  • tt is the time the money is invested for, in years, which is 8 years.

Let's calculate the future value.After 8 years, with a monthly compounded interest rate of 10%, your capital would grow to approximately ₹470,61,71,826 (about 470.6 crores).

Would you like to know more details or have any questions? Here are some related questions you might find interesting:

  1. How would the capital differ if the interest rate was compounded quarterly instead of monthly?
  2. What would be the future value if the interest rate was 8% monthly instead of 10%?
  3. How does the length of the investment period affect the final amount?
  4. What is the formula for continuous compounding, and how would the result change with continuous compounding?
  5. Can you explain how the concept of compounding applies to real-world investment scenarios?

Tip: When dealing with high-interest rates, frequent compounding significantly boosts the growth of your investment over time.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

Compound Interest Formula A = P (1 + r/n)^(nt)

Theorems

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Suitable Grade Level

Advanced High School