our credit card has a balance of ​$5800


and an annual interest rate of 18
​%.
You decide to pay off the balance over three

years. If there are no further purchases charged to the​ card,
a. How much must you pay each​ month?
b. How much total interest will you​ pay?

To calculate how much you need to pay each month and the total interest paid over three years, we can use the formula for calculating the monthly payment amount for a fixed-term loan. The formula is:

Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:
P = Principal balance (credit card balance)
r = Monthly interest rate (annual interest rate divided by 12 and then divided by 100)
n = Total number of payments (in this case, 3 years multiplied by 12 months per year)

Let's calculate it step by step.

a. How much must you pay each month?

First, convert the annual interest rate to a monthly interest rate:
Monthly interest rate = 18% / 12 / 100 = 0.015

Now, calculate the total number of payments:
Number of payments = 3 years * 12 months/year = 36

Now, let's plug these values into the formula:

Monthly Payment = $5800 * (0.015 * (1 + 0.015)^36) / ((1 + 0.015)^36 - 1)

Using a calculator, we can simplify this calculation to find the monthly payment amount.

b. How much total interest will you pay?

Total interest paid = (Monthly Payment * Number of payments) - Principal balance

Now, let's calculate the total interest paid using the monthly payment amount we calculated in part a:

Total interest paid = (Monthly Payment * 36) - $5800

By plugging in the monthly payment amount, we can find the total interest paid.

Keep in mind that this calculation assumes no additional purchases and that the interest rate remains constant over the three-year period.