Final Answer:
The total cost to repay the one-month long short-term loan with a principal of $550 and an interest rate of 350% APR is $612.32.
The correct option is d) $612.32.
Step-by-step explanation:
To find the total cost to repay a short-term loan, we use a loan calculator that takes into account the principal, interest rate, and compounding frequency. In this case, the loan has a principal of $550, an interest rate of 350% APR (which is equivalent to an annual interest rate of 42%), and a one-month term (equivalent to 1/12 of a year).
Using a loan calculator, we input these values and select monthly compounding (which means interest is calculated and added to the principal at the end of each month). The calculator then shows us that the monthly payment is $612.32, and the total cost to repay the loan (principal plus interest) is $612.32.
Here's how we arrived at this answer:
First, we convert the APR to an annual interest rate by dividing it by 12 (since there are 12 months in a year):
Annual interest rate = APR / 12 = 350% / 12 = 29.17%
Next, we calculate the monthly interest rate by dividing the annual interest rate by 12:
Monthly interest rate = Annual interest rate / 12 = 29.17% / 12 = 2.43%
Then, we calculate the monthly payment using the formula:
Monthly payment = Principal / [(1 + Monthly interest rate) ^ (Number of payments) - 1] / (Monthly interest rate * (1 + Monthly interest rate) ^ (Number of payments - 1))
Substituting our values into this formula:
Monthly payment = $550 / [(1 + 0.0243) ^ 1 - 1] / (0.0243 * (1 + 0.0243) ^ (1 - 1)) = $612.32
Finally, we calculate the total cost to repay the loan by multiplying the monthly payment by the number of payments:
Total cost to repay = Monthly payment * Number of payments = $612.32 * 1 = $612.32
Therefore, The correct option is d) $612.32.