Question

To pay for a home improvement project that totals $16,000, Genesis is choosing between taking out a simple interest bank loan at 8% for 3 years or paying with a credit card that compounds monthly at an annual rate of 15% for 7 years. Which plan would give Genesis the lowest monthly payment?

The monthly credit card payment would be $511.11, which is lower than the monthly payment on the bank loan.

The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.

The monthly payment on a bank loan would be $551.11, which is lower than the monthly credit card payment.

The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.

Answer 1

Answer: The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.

To calculate the monthly payment on the bank loan, we can use the formula:

monthly payment = P * (r / (1 - (1 + r)^(-n)))

where P is the total loan amount, r is the annual interest rate as a decimal, and n is the number of months of the loan.

For a loan of $16,000 at 8% interest for 3 years (36 months)

r = 0.08/12 = 0.0067

n = 36

P = 16000

So, the monthly payment = 16000 * (0.0067 / (1 - (1 + 0.0067)^(-36))) = 480

To calculate the monthly credit card payment, we can use the formula:

M = P * r * (1 + r)^n / [(1 + r)^n - 1]

where P is the total loan amount, r is the monthly interest rate, and n is the number of months of the loan.

For a credit card with an annual rate of 15% for 7 years (84 months)

r = 0.15/12 = 0.0125

n = 84

P = 16000

So, the monthly payment = 16000 * 0.0125 * (1 + 0.0125)^84 / [(1 + 0.0125)^84 - 1] = 511.11

As we can see the monthly payment on the bank loan is lower than the monthly credit card payment. So, the correct answer is "The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment."