The Equivalent Annual Growth Rate of a 0.5% Monthly Growth Rate

What is the annual growth rate equivalent of a monthly growth rate of 0.5%?

Final answer: The equivalent annual growth rate of a 0.5% monthly growth rate, accounting for compound interest, is 6.17%. Simply multiplying the monthly rate by 12 would yield an inaccurate result. The correct process involves raising the total monthly rate to the 12th power, subtracting 1, and then converting back to a percentage.

Understanding Compound Interest and Annual Growth Rate Calculation

Compound interest is the concept of earning interest on both the initial principal amount and the accumulated interest from previous periods. This is in contrast to simple interest, where interest is only earned on the principal amount.

Calculating Annual Growth Rate from Monthly Growth Rate

When calculating the equivalent annual growth rate from a monthly growth rate, it is essential to consider the compounding effect over time. Simply multiplying the monthly growth rate by 12 would not give an accurate annual growth rate as it ignores the compounding nature of interest.

To accurately calculate the annual growth rate from a monthly rate, the following formula can be used:

(1 + Monthly Growth Rate) ^ 12 - 1

Let's apply this formula to the given monthly growth rate of 0.5%:

(1 + 0.005) ^ 12 - 1 = (1.005) ^ 12 - 1 = 1.0617 - 1 = 0.0617

Converting this result back to a percentage:

0.0617 x 100 = 6.17%

Therefore, the equivalent annual growth rate of a 0.5% monthly growth rate is 6.17%, which corresponds to option (d) in the multiple-choice question.

Understanding the power of compounding and applying the correct formula is crucial in accurately determining annual growth rates from monthly values.