25 An electronics retaller charges customers an anniual interest rate of [6m] a) convert \( 31.4 \% \) to a decimal. Divide this number by the number of days in 1 year to determine the dally interest rate charged. Round your answer to 5 decimal places. b) Calculate the interest charged in 1 day. on an unpaid balance of \( \$ 7000 \). c) Compare this amount to the interest earned in. 1 year in 1 of your researched savings accounts.

Let's solve the problem step by step. ### Part a: Convert \( 31.4\% \) to a decimal and find the daily interest rate 1. **Convert \( 31.4\% \) to a decimal:** \[ \text{Decimal} = \frac{31.4}{100} = 0.314 \] 2. **Calculate the daily interest rate:** - There are \( 365 \) days in a year. \[ \text{Daily Interest Rate} = \frac{0.314}{365} \] Now, let's calculate the daily interest rate and round it to 5 decimal places. ### Part b: Calculate the interest charged in 1 day on an unpaid balance of \( \$7000 \) 1. **Use the daily interest rate to find the interest charged in 1 day:** \[ \text{Interest Charged in 1 Day} = \text{Daily Interest Rate} \times 7000 \] ### Part c: Compare this amount to the interest earned in 1 year in a researched savings account For this part, I will need to assume a typical savings account interest rate. Let's say the average savings account interest rate is \( 1.5\% \) annually. 1. **Convert \( 1.5\% \) to a decimal:** \[ \text{Savings Account Decimal} = \frac{1.5}{100} = 0.015 \] 2. **Calculate the interest earned in 1 year on \( \$7000 \):** \[ \text{Interest Earned in 1 Year} = 7000 \times 0.015 \] Now, let's perform the calculations for parts a and b. Calculate the value by following steps: - step0: Calculate: \(7000\times 0.015\) - step1: Multiply the numbers: \(105\) Calculate or simplify the expression \( 0.314/365 \). Calculate the value by following steps: - step0: Calculate: \(\frac{0.314}{365}\) - step1: Convert the expressions: \(\frac{\frac{157}{500}}{365}\) - step2: Multiply by the reciprocal: \(\frac{157}{500}\times \frac{1}{365}\) - step3: Multiply the fractions: \(\frac{157}{500\times 365}\) - step4: Multiply: \(\frac{157}{182500}\) Calculate or simplify the expression \( (0.314/365)*7000 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{0.314}{365}\right)\times 7000\) - step1: Divide the terms: \(\frac{157}{182500}\times 7000\) - step2: Reduce the numbers: \(\frac{157}{365}\times 14\) - step3: Multiply: \(\frac{157\times 14}{365}\) - step4: Multiply: \(\frac{2198}{365}\) ### Part a: Daily Interest Rate Calculation 1. **Daily Interest Rate:** \[ \text{Daily Interest Rate} \approx 0.00086 \] (rounded to 5 decimal places: \( 0.00086 \)) ### Part b: Interest Charged in 1 Day 1. **Interest Charged in 1 Day:** \[ \text{Interest Charged in 1 Day} \approx 6.02192 \] ### Part c: Interest Earned in 1 Year in a Savings Account 1. **Interest Earned in 1 Year:** \[ \text{Interest Earned in 1 Year} = 105 \] ### Summary of Results - **Daily Interest Rate:** \( 0.00086 \) - **Interest Charged in 1 Day on \( \$7000 \):** \( \approx 6.02 \) - **Interest Earned in 1 Year on \( \$7000 \) in a Savings Account:** \( 105 \) ### Comparison - The interest charged in 1 day on an unpaid balance of \( \$7000 \) is approximately \( 6.02 \). - The interest earned in 1 year in a typical savings account is \( 105 \). This shows that the interest charged by the electronics retailer is significantly higher than the interest earned in a savings account over the same period.