The first step is to calculate the total cost for each option.
For the bank loan, we need to calculate the interest amount and add it to the principal (the original amount borrowed). The interest is calculated using simple interest, which means it is a fixed percentage of the principal. In this case, the interest rate is 5% per year for 3 years.
To calculate the total cost of the bank loan, we multiply the principal ($6500) by the interest rate (0.05) and the number of years (3). Then we add the result to the principal:
Total Cost of Bank Loan = Principal + (Principal * Interest Rate * Number of Years)
= $6500 + ($6500 * 0.05 * 3)
= $6500 + $975
= $7475
Now let's calculate the total cost for the credit card option. The interest on the credit card compounds monthly, which means it is calculated based on the previous balance plus the interest. The interest rate is 15% per year.
To calculate the total cost of the credit card, we need to use a formula called the compound interest formula. The formula is:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the principal is $6500, the interest rate is 15% per year, the interest is compounded monthly (so n = 12), and the number of years is 3.
Total Cost of Credit Card = Principal * (1 + Interest Rate/Number of Compounding Periods)^(Number of Compounding Periods * Number of Years)
= $6500 * (1 + 0.15/12)^(12 * 3)
= $6500 * (1 + 0.0125)^(36)
To find the lowest monthly payment, we need to divide the total cost of each option by the number of months in 3 years (36 months).
Monthly Payment for Bank Loan = Total Cost of Bank Loan / Number of Months
= $7475 / 36
= $207.64 (rounded to the nearest cent)
Monthly Payment for Credit Card = Total Cost of Credit Card / Number of Months
= ($6500 * (1 + 0.0125)^(36)) / 36
= $215.17 (rounded to the nearest cent)
Therefore, the bank loan option will give Roger the lowest monthly payment at approximately $207.64