Question

Suppose you owe ​$600 on your credit card and you decide to make no new purchases and to make the minimum monthly payment on the account. Assuming that the interest rate on your card is 1​% per month on the unpaid balance and that the minimum payment is 2​% of the total​ (balance plus​ interest), your balance after t months is given by ​B(t)=600​(0.9898t​). Find your balance at each of the given times. Complete parts​ (a) through​ (e) below.

​(a) six months

After six​ months, the balance is

​(Round to the nearest cent as​ needed.)

​(b) one year​ (remember that t is in​ months)

After one​ year, the balance is

​(Round to the nearest cent as​ needed.)

​(c) five years After five ​years, the balance is

​(Round to the nearest cent as​ needed.)

​(d) nine years After nine ​years, the balance is

​(Round to the nearest cent as​ needed.)

​(e) On the basis of your answers to parts ​(a)–​(d), what advice would you give to your friends about minimum​ payments?

A. The minimum payment minimizes the​ short-term cost and maximizes the​ long-term cost. It would be advisable to pay only the minimum monthly payment to decrease the​ short-term cost.

B. The minimum payment maximizes the​ short-term cost and minimizes the​ long-term cost. It would be advisable to pay more than the minimum monthly payment when possible to decrease the overall cost.

C. The minimum payment maximizes the​ short-term cost and minimizes the​ long-term cost. It would be advisable to pay only the minimum monthly payment to decrease the​ short-term cost.

D. The minimum payment minimizes the​ short-term cost and maximizes the​ long-term cost. It would be advisable to pay more than the minimum monthly payment when possible to decrease the overall cost

Answer 1

Answer

B(t)=600(0.9898^t) $ 600.00 1% a Amount Owed Interest rate Month (0) After 6 month balance is 6 month 564.20 =600*(0.989846) $ 600.00 1% b Amount Owed Interest rate Month (t) After one year balance is 12 month $ 530.54 =600*(0.9898-12) $ c Amount Owed Interest rate Month(t) After five year balance is 600.00 1% (12*5) 324.34 =600*(0.9898460) 60 month $ d Amount Owed Interest rate Month (t) After nine year balance is $ 600.00 1% 108 month 12*9 198.28 =600*(0.9898-108) e Advice to be given to friends about minimum payments Correct Answer is D. The minimum payment minimizes the short-term cost and maximizes the long-term cost. It would be advisable to pay more than the minimum monthly payment when possible to decrease the overall cost As the interest keeps on increaing so long term interest keeps on incrasing. So it is better to pay more than minimum monthly payment to decrease total interest cost

.