Calculating Compound Interest for Monthly Deposits with Quarterly Compounding

Ken decides to open a savings account at ABC Bank, which offers a 2% annual interest rate compounded quarterly. He plans to deposit P3000 every month. Let's determine the total amount Ken will have in his account at the end of 5 years.

Understanding the Compounding Interest Principle

When an interest rate is compounded, it means that the interest earned in each period is added to the principal, and the next period's interest is calculated on this new amount. In Ken's case, the interest is compounded quarterly, which means it is applied four times a year. To accurately calculate the future value of his monthly deposits, we need to convert these monthly deposits into an equivalent quarterly contribution.

Step-by-Step Calculation

Step 1: Convert Monthly Deposits to Quarterly

Since Ken deposits P3000 every month, over a quarter (3 months), he will deposit:

Quarterly Deposit P3000 times; 3 P9000

Step 2: Determine the Number of Quarters

In 5 years, there are:

Total Quarters 5 years times; 4 quarters/year 20 quarters

Step 3: Calculate the Future Value of a Series

The future value of a series can be calculated using the future value of a series formula:

FV P times; (1 r^n - 1) / r

In this context, P is the amount deposited per period (quater), r is the interest rate per period, and n is the total number of periods.

Step 4: Calculate the Interest Rate per Quarter

The annual interest rate is 2%, so the quarterly interest rate (r) is:

r 2 / 4 0.5% 0.005

Step 5: Calculate the Future Value

Substitute the values into the future value formula:

FV P9000 times; (1 0.005^n - 1) / 0.005

First, calculate:
1 0.005^20 - 1 ≈ 1.104622

Now, substitute this back into the future value formula:

FV P9000 times; (1.104622 - 1) / 0.005

Calculate the value inside the parentheses:

FV P9000 times; 0.104622 / 0.005

Calculate the final amount:

FV ≈ P9000 times; 20.9244 ≈ P188319.60

Conclusion

At the end of 5 years, Ken will have approximately P188,319.60 in his bank account. This calculation helps us understand how compound interest and regular contributions can significantly grow an investment over time.

Adjusting for Quarterly Compounding

Another approach to calculating the future value involves converting the interest rate to a quarterly equivalent. The equivalent monthly interest rate can be derived as follows:

(1 2/400^1/3 - 1) times; 1200 ≈ 1.99667592

Using this adjusted rate, the future value of the investments can be calculated as:

FV 3000 [{1 1.99667592/1200^5 12 - 1} ÷ 1.99667592/1200] ≈ 189126.38

Both methods confirm that regular monthly deposits, when compounded quarterly, can lead to substantial growth in investment over time.

Conclusion

This example demonstrates the power of compound interest and regular contributions. It's crucial to understand the periodic interest rate and the number of compounding periods to accurately calculate the future value of an investment. Whether using the future value of a series formula or adjusting rates for compounding, the results are consistent and provide valuable insights into financial planning.

By following these steps and understanding the principles of compound interest, individuals like Ken can make informed decisions about saving and investing for their future financial needs.