Introduction

When it comes to savings accounts, the frequency of compounding can significantly impact the growth of your investment over time. This article aims to compare two types of savings accounts: one that compounds interest annually and another that compounds it continuously. We will analyze their performance over a ten-year period and extend the analysis to longer investment horizons to determine which type of account offers a better return in the long term.

Understanding Compounding Frequencies

Compounding is the process of earning interest on both the principal amount and the accumulated interest over time. The frequency of compounding can be annual, monthly, or even continuously. The more frequently the interest is compounded, the faster the account balance will grow, all else being equal.

Compounded Annually

The formula for the future value A of an investment compounded annually is:

A P(1 r) harvested_time

Where:

P the principal amount (initial investment) r the annual interest rate (in decimal form) t the number of years the money is invested for

Compounded Continuously

The formula for the future value A of an investment compounded continuously is:

A Pert

Where:

e is the base of the natural logarithm, approximately equal to 2.71828 P, r, and t are the same as defined above

Example Calculation

Let's assume an initial investment of P 1000 for both accounts and compare them over t 10 years using an annual interest rate of r 0.05.

Compounded Annually

The formula for annual compounding is:

A P(1 r)10

Plugging in the values:

A 1000(1 0.05)10

A ≈ 1000(1.62889)

A ≈ 1628.89

Compounded Continuously

The formula for continuous compounding is:

A Pert

Plugging in the values:

A 1000e0.05 × 10

A ≈ 1000e0.5

A ≈ 1000(1.64872)

A ≈ 1648.72

Conclusion

After 10 years:

Compounded Annually: Approximately $1628.89 Compounded Continuously: Approximately $1648.72

Thus, the second savings account, which pays 5% compounded continuously, is a better investment in the long term. The difference in returns becomes more pronounced as the investment period increases. In fact, the continuously compounded 5% account will grow at the same rate as an annually-compounded 5.127% account.

Practical Considerations

In practice, banks in India, for example, typically credit interest on a quarterly basis. This means that a savings account that pays interest quarterly is more beneficial than one that pays annually. If a bank offers compounding on a daily basis based on the average of the minimum-maximum balances on a monthly or quarterly basis, it offers even better returns, though such arrangements are less common.

Bank Policies and Guidelines

According to the Reserve Bank of India (RBI), banks in India are required to credit interest on savings accounts on a quarterly basis. This automatic compounding further enhances the returns on your investment. If you do not withdraw the interest amount, it is compounded automatically, leading to a higher final balance over time.

In summary, the choice between an annually-compounded and continuously-compounded savings account depends on the specific compounding frequency offered by the bank and the length of the investment horizon. In most practical scenarios, a savings account with more frequent compounding, such as quarterly, would be the better investment option.