Suppose you owe $1,000 on your credit card. The annual percentage rate (APR) is
ID: 2640570 • Letter: S
Question
Suppose you owe $1,000 on your credit card. The annual percentage rate (APR) is 24%, compounded monthly. The credit card company says your minimum monthly payment is $22.39. a. If you make only this minimum payment, how long will it take for you to repay the $1,000 balance (assuming no more charges are made)? b. If you make the minimum payment plus $9.07 extra each month (for a total of $31.46), how long will it take to repay the $1,000 balance? c. Compare the total interest paid in Part (a) with the total interest paid in Part (b).Explanation / Answer
a) As per the inputs given above, we need to pay 1000 to the company with interest rate of 24%. Thus monthly interest income would come out to be = 1000*(24/12)% = 20
Minimum monthly payment = 22.39
Using NPER function in excel to calculate months to payoff the 1000 amount, we get NPER(rate, PMT,pv)
=NPER(24/12%,22.39,-1000) = 112.98 months = 9.42 years
b) Minimum monthly payment = 9.07+22.39 = 31.46
Using same NPER function, we get months to pay off as 51 months = 4.25 years
c) Total interest paid is calculated as Months*monthly payment- Initial amount due
Total interest paid in Part a = 112.98*22.39-1000 = 1529.65
Total interest paid in Part b = 51*31.46 -1000 = 604.33
Thus, we see that when we increase the monthly payment and pay the amount due earlier, we pay less interest on the amount owed.
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