Question

Suppose you owe $900 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 2​% per month on the unpaid balance and that the minimum payment is 3​% of the total​ (balance plus​ interest), your balance after t months is given by ​B(t)=900​(0.9894t​).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) seven years

After seven 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 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.

B.

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.

C.

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.

D.

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.

Answer 1

option (C) CORRECT SUGGESTION

Minimum payment out of the due will lead to high interest on the due and the net payable Balance (shown here below will drastically increase ) from 900$ to 96170$ in 9years

One should pay more than the minimum payment amount to avoid high longterm cost

calculation of B(t) based on the equation mention above can be seen in the notes below ,

for initial for one month

owe amount =$900 ,

interest = (900 x .02 x 1) here .02 is nothing but 2%

interest =$18

total =900+18 =$ 918 ( balance+interest)

minimum amount to be paid = $27.54 (ie 0.03 x 918)

unpaid amount after 1 month = 890.46( ie. 918-27.54 ) , this Unpaid amount or B(t) can be calculated using the equation B(t) directly , calculation for different time period mentioned in the question and there conclusion is shown below

considering the fact that we only pay the minimum payment required to be paid the balance is calculated after each mentioned term , with interest adding to it the balance grows with time ahead as shown below

now for 9years , t=108 (ie 9x12 months) in the same equation ie B(t) = 900(0.9894 x 108)

B(t) after 9years can be calculated as shown below showing that balance actually increase drastically if one only pays the minimum payment balance every month leaving the rest as dues

Minimum payment minimize the short term cost and maximize the longterm cost because interest on the due always add on to the unpaid amount hence advice to pay more than the minimum payment needed to avoid high longterm cost