# Compound Interest Fun Fact!

## What is the effect rate of 5% interest compounding quarterly?

a. 5%

b. 5.12%

c. 5.09%

d. 5.06%

## The effect rate of 5% interest compounding quarterly is 5.12%.

Explanation: The effect rate of 5% interest compounding quarterly can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we have P = 1, r = 5% (or 0.05), and n = 4 (quarterly compounding). Plugging in these values, we get: A = 1(1 + 0.05/4)^(4t). Simplifying further, we have: A = 1.05^(4t). Therefore, the effect rate of 5% interest compounding quarterly is 5.12% (option b).

## Understanding Compound Interest Fun Fact!

**Compound interest can be a fun topic to explore, especially when you discover interesting facts like the effect rate of a 5% interest compounding quarterly!** When dealing with compound interest, remember that the frequency of compounding plays a crucial role in the final amount you'll receive. In this case, the effect rate of 5% interest compounding quarterly is calculated to be 5.12%, offering a slightly higher return compared to the nominal rate.

By utilizing the compound interest formula and understanding the variables involved, you can uncover fascinating phenomena like the increase in the effect rate due to quarterly compounding. This example highlights the power of compounding and the impact it can have on your investments over time.

So, the next time you come across a compound interest question or fact, remember to dive into the details and discover the hidden treasures of financial mathematics. Who knows what exciting facts and insights you may uncover along the way!