The payday loan company's rate is 16% every two weeks. There are 26 two-week periods in a year. Ehat total percent would this be in a year?

To calculate the annual percentage rate (APR) from a two-week interest rate of 16%, we need to account for the compounding effect over the year.

The formula to convert a periodic interest rate to an annual rate (with compounding) is:

\[
\text{APR} = \left(1 + \frac{r}{100}\right)^n - 1
\]

Where:
- \(r\) is the interest rate for the period (in this case, 16% every two weeks).
- \(n\) is the number of periods in a year (26 two-week periods).

Let's calculate this:

\[
\text{APR} = \left(1 + \frac{16}{100}\right)^{26} - 1
\]

Now, I'll compute this.The annual percentage rate (APR) when compounded every two weeks at 16% is approximately **4641.41%**. This extremely high value reflects the effect of compounding frequently at a very high interest rate.

Would you like further details or have any questions?

Here are five related questions to consider:
1. What is the difference between simple interest and compound interest?
2. How does the frequency of compounding impact the total amount of interest?
3. How would the APR change if the two-week rate were lower?
4. What is the formula for calculating continuous compounding interest?
5. How can compounding lead to debt accumulation in payday loans?

**Tip:** When dealing with high-interest short-term loans, always consider the effects of compounding, as it can lead to much higher annual rates than it seems at first.

The payday loan company's rate is 16% every two weeks. There are 26 two-week periods in a year. What total percent would this be in a year?

Learn how to calculate the annual percentage rate (APR) from a 16% two-week interest rate on a payday loan. Using the compound interest formula, this problem demonstrates the exponential growth of interest, leading to an APR of over 4600%. Suitable for students in Grades 11-12.

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