Question

#1 -Suppose you owe $3500 on a credit card that charges 16.83% interest. How much would you pay each month if you paid the card off in 3 years?

#2-Using the same problem as question #1, how long would it take to pay the balance off if you spent only $50 per month?

Answer 1

Explanation:

#1 - To calculate the monthly payment required to pay off a $3500 credit card balance with a 16.83% interest rate in 3 years, we can use the formula for calculating the monthly payment on a fixed-rate loan:

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

where: M = monthly payment P = principal (the amount owed) r = monthly interest rate (16.83% / 12 = 0.014) n = total number of payments (3 years * 12 months/year = 36)

Plugging in the values, we get:

M = 3500 * (0.014 * (1 + 0.014)^36) / ((1 + 0.014)^36 - 1) = $123.39

Therefore, the monthly payment required to pay off the $3500 credit card balance in 3 years is $123.39.

#2 - To calculate how long it would take to pay off the $3500 credit card balance by making only $50 monthly payments, we can use the formula:

n = -(1/30) * log(1 - ((r * P) / M))

where: n = number of months to pay off the balance r = monthly interest rate (16.83% / 12 = 0.014) P = principal (the amount owed) M = monthly payment ($50)

Plugging in the values, we get:

n = -(1/30) * log(1 - ((0.014 * 3500) / 50)) = 144.6

Therefore, it would take approximately 145 months (or 12 years and 1 month) to pay off the $3500 credit card balance by making only $50 monthly payments.

Answer 2

Explanation:

#1 - To calculate the monthly payment required to pay off a $3500 credit card balance with a 16.83% interest rate in 3 years, we can use the formula for calculating the monthly payment on a fixed-rate loan:

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

where: M = monthly payment P = principal (the amount owed) r = monthly interest rate (16.83% / 12 = 0.014) n = total number of payments (3 years * 12 months/year = 36)

Plugging in the values, we get:

M = 3500 * (0.014 * (1 + 0.014)^36) / ((1 + 0.014)^36 - 1) = $123.39

Therefore, the monthly payment required to pay off the $3500 credit card balance in 3 years is $123.39.

#2 - To calculate how long it would take to pay off the $3500 credit card balance by making only $50 monthly payments, we can use the formula:

n = -(1/30) * log(1 - ((r * P) / M))

where: n = number of months to pay off the balance r = monthly interest rate (16.83% / 12 = 0.014) P = principal (the amount owed) M = monthly payment ($50)

Plugging in the values, we get:

n = -(1/30) * log(1 - ((0.014 * 3500) / 50)) = 144.6

Therefore, it would take approximately 145 months (or 12 years and 1 month) to pay off the $3500 credit card balance by making only $50 monthly payments.