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Answer :
Amanda is being charged a nominal interest rate of approximately 0.05127% per day on her credit card.
To find the nominal interest rate charged on Amanda's credit card, we can use the formula for the monthly payment on an amortized loan:
Monthly Payment = Principal * (r * (1+r)^n) / ((1+r)^n - 1)
Where:
- Principal is the initial loan amount ($5,915)
- r is the monthly interest rate (to be determined)
- n is the total number of payments (5 years * 12 months per year = 60 payments)
We know that Amanda's monthly payment is $185.78. Let's plug in these values and solve for the monthly interest rate (r):
$185.78 = $5,915 * (r * (1+r)^60) / ((1+r)^60 - 1)
To solve this equation, we can use numerical methods or an online calculator. Solving it, we find that the monthly interest rate (r) is approximately 0.0156, or 1.56%.
Since the interest is compounded daily, we need to convert the monthly interest rate to a daily rate. We can do this by dividing the monthly rate by the average number of days in a month:
Daily Interest Rate = Monthly Interest Rate / Average Number of Days in a Month
Assuming there are 365 days in a year, the average number of days in a month is approximately 365 / 12 = 30.42. Let's calculate the daily interest rate:
Daily Interest Rate = 0.0156 / 30.42
The daily interest rate is approximately 0.0005127, or 0.05127%.
Therefore, Amanda is being charged a nominal interest rate of approximately 0.05127% per day on her credit card.
Learn more about nominal interest rate here;
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