Calculating Compound Interest on Rs 15625 with Interest Composed Every 8 Months

In this article, we will discuss how to calculate the compound interest on a sum of Rs 15625 for 2 years with an interest rate of 2% per annum, compounded every 8 months. Understanding the steps involved can help you tackle similar problems efficiently.

Understanding Compound Interest and Compounding Periods

Compound interest is a method of calculating interest based on the initial amount (principal) and the interest accumulated over time. When the interest is compounded, it means that the interest is added to the principal at regular intervals, and the next period's interest is calculated on the new principal amount. This process can be applied every 8 months in this case.

Step-by-Step Calculation

Step 1: Determine the Number of Compounding Periods

Since the interest is compounded every 8 months, we first need to calculate how many 8-month periods are there in 2 years. The number of months in 2 years is 24. The number of compounding periods is calculated as follows:

Number of compounding periods 24 months / 8 months 3

Step 2: Calculate the Effective Interest Rate Per Period

The annual interest rate is given as 2%. Since the interest is compounded every 8 months, we need to find the interest rate for each 8-month period. The formula to find the effective interest rate per period is:

Interest rate for 8 months 2 / 1.5 1.3333

Step 3: Use the Compound Interest Formula

The formula for compound interest is:

A P * (1 r/100)n

Where:

A the amount of money accumulated after n years including interest P the principal amount (initial investment) r annual interest rate in percentage n number of compounding periods

In our case, P 15625, r 1.3333 for each 8 months, and n 3. Substituting these values into the formula, we get:

A 15625 * (1 1.3333/100)3

Step 4: Calculate the Total Amount

First, we need to calculate the value inside the parentheses:

1 1.3333/100 1.013333

Now, we need to find the value of 1.013333 raised to the power of 3:

1.0133333 1.0404

Now, substituting back into the compound interest formula:

A ≈ 15625 * 1.0404 ≈ 16266.25

Step 5: Calculate the Compound Interest

Compound interest (CI) is given by:

CI A - P

So, the compound interest is:

CI 16266.25 - 15625 641.25

Final Answer

The compound interest on the sum of Rs 15625 for 2 years at the rate of 2% per annum, compounded every 8 months, is approximately Rs 641.25.

Alternatively, using a simplified approach:

Principal 15625

Rate per year 2% 0.02

Interest paying term every 8 months for 2 years 2 * (12/8) 3

Amount after 2 years 15625 * (1 0.02*(8/12))^3 ≈ 16258.37

Interest after 2 years 16258.37 - 15625 ≈ 633.37

Answer: Rs 633.37

Understanding these calculations can help you manage and grow your investments more effectively. Whether you're planning to calculate compound interest for a personal loan, savings account, or larger investment, this method will serve you well.