Thank you for visiting You can buy an item for 125 on a charge with the promise to pay 125 in 60 days Suppose you can buy an identical. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To calculate the effective annual rate of interest, we first need to determine the interest rate for the 60-day period, then convert it to an annual rate.
Identify Known Values:
- Cash price of the item: $115
- Charge price of the item: $125
- Duration: 60 days
- Interest paid for 60 days: $125 - $115 = $10
Calculate the Interest Rate for 60 Days:
The formula to calculate simple interest is:
[tex]\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}[/tex]In this case, we can rearrange the formula to find [tex]\text{Rate}[/tex]:
[tex]\text{Rate} = \frac{\text{Interest}}{\text{Principal} \times \text{Time}}[/tex]Substitute the known values:
[tex]\text{Rate} = \frac{10}{115 \times \frac{60}{365}}[/tex]Simplifying gives:
[tex]\text{Rate} = \frac{10}{115 \times \frac{60}{365}} \approx 0.05217[/tex]Convert to an Annual Rate:
Since the rate is calculated for 60 days, we need to annualize it. To do so, multiply by the number of 60-day periods in a year:
[tex]\text{Annual Rate} = 0.05217 \times \frac{365}{60} \approx 0.317[/tex]Express the Result as a Percentage:
Convert the decimal format to a percentage by multiplying by 100:
[tex]\text{Effective Annual Rate} = 0.317 \times 100 \approx 31.70\%[/tex]
Therefore, the effective annual rate of interest is 31.70%.
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