Calculating Compound Interest Rate for a Given Amount

The compound interest rate is a crucial concept in finance for understanding how investments grow over time, or how loans yield interest. In this project, we explore how to find the annual compound interest rate using a specific scenario. Let's break down the problem of determining the rate per annum that will cause Rs. 5000 to amount to Rs. 5832 in 2 years compounded annually.

Understanding Compound Interest

Compound interest is a type of interest that is calculated on the initial principal and the accumulated interest from previous periods. It allows the borrower to pay interest only on the initial amount borrowed and not on the interest previously accrued, leading to exponential growth over time.

Step-by-Step Solution: Finding the Annual Compound Interest Rate

We start with the formula for compound interest, which is given by:

[A P left(1 frac{r}{100}right)^n]

Where: (A) is the amount of money accumulated after n years, including interest. (P) is the principal amount (the initial sum of money). (r) is the annual interest rate (in percent). (n) is the number of years the money is invested or borrowed for.

Given Values and Formula Application

In our scenario, we have:

(A 5832) (P 5000) (n 2)

Substituting these values into the formula, we get:

[5832 5000 left(1 frac{r}{100}right)^2]

Now, we solve for (r):

Divide both sides by 5000:

[frac{5832}{5000} left(1 frac{r}{100}right)^2]

Calculate the left side:

[1.1664 left(1 frac{r}{100}right)^2]

Take the square root of both sides:

[1 frac{r}{100} sqrt{1.1664}]

Calculate the square root:

[1 frac{r}{100} approx 1.08]

Subtract 1 from both sides to find (r):

[frac{r}{100} approx 0.08]

Convert this into a percentage:

[r approx 8%]

Hence, the annual compound interest rate is 8%.

Alternative Applications and Related Concepts

Compound interest is not just confined to financial investments; it can also be applied to investments like house loans, car loans, and other financial instruments. The compounded interest rate is often used to determine the future value of an investment or the total repayment amount for a loan. For example, if an individual wishes to calculate the rate of return on an asset or investment, the concept of Compound Annual Growth Rate (CAGR) can be used, which is another form of the compound interest formula rearranged to solve for the rate of return.

Understanding and calculating the annual compound interest rate is essential for both investors and borrowers. It helps in making informed financial decisions and planning long-term investments or loan repayments.

Conclusion

In conclusion, the annual compound interest rate per annum that will cause Rs. 5000 to amount to Rs. 5832 in 2 years compounded annually is 8%. This rate can be calculated using the compound interest formula, making it a valuable tool for financial analysis and planning.

Keywords: compound interest rate, annual interest rate, compound interest formula