Question

Yout roommate let you borrow $256 to buy the PS5 4 months ago. You just paid him back today and gave him $20 extra for intarest What is the period rate? Convert to a percont, round to 2 decimal places QUESTION 5 Your roomnate let you borrow 5308 to buy the PS5 6 monthe ago. You just paid him back today and gave him $35 extra for interent. What is the annuat percentage rate (APR)? Convert to a percent, found to 2 docimal places QUESTION 6 You are late paying your cable bil again. It was due 10 days ago and you have been charged $37. Your bil was $105. What is the annial percentage rate (APR)? Convert to a percent and round to 2 decimal places.

Answer 1

For Question 5, the period rate is 3.78%, and for Question 6, the annual percentage rate (APR) is 47.92%.

Step-by-step explanation:

In Question 5, to find the period rate, you can use the formula for simple interest:

`\[ \text{Period Rate} = \frac{\text{Interest Paid}}{\text{Principal} * \text{Number of Periods}} \]`

Substituting the given values, where Interest Paid is $20, Principal is $256, and Number of Periods is 4 months, we get:

`\[ \text{Period Rate} = (20)/(256 * 4) \]`

Calculating this gives a period rate of 0.01953. To convert this to a percentage, you multiply by 100, rounding to two decimal places, resulting in a period rate of 1.95%.

For Question 6, to find the annual percentage rate (APR), you can use the formula:

`\[ \text{APR} = \left(1 + \frac{\text{Period Rate}}{\text{Number of Periods}}\right)^{\text{Number of Periods} * \text{Periods in a Year}} - 1 \]`

Substituting the values where Period Rate is 0.01953 and Number of Periods is 6 months, we get:

`\[ \text{APR} = \left(1 + (0.01953)/(6)\right)^(6 * 12) - 1 \]`

Calculating this gives an APR of 0.4792. To convert this to a percentage, you multiply by 100, rounding to two decimal places, resulting in an APR of 47.92%.

In both cases, these calculations provide the interest rates in the requested formats.