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marishachu [46]
3 years ago
15

Martin's unpaid credit card balance was $1539.39. his APR is 13.2%. what is his new balance after he makes one new transaction f

or $178
$1486.48
$1556.32
$1734.32
$1920.59
Mathematics
1 answer:
irinina [24]3 years ago
4 0
Given that <span>Martin's unpaid credit card balance was $1539.39 and his APR is 13.2%.

APR is the annual interest rate, to get the monthly interest rate, we divide the APR by 12.

Thus, monthly interest rate is </span>i= \frac{13.2\%}{12} =1.1%

The interest charge for the month is given by I=Pi, where P is the previous balance, i is the monthly interest rate.

Thus, interest charge is I=1,539.39(0.011)=1,539.39(0.011)=\$16.93

The balance after the monthly interest charge = $1,539.39 + $16.93 = $1,556.32

Therefore, the balance after the new transaction is given by $1,556.32 + $178 = $1734.32
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The sum of the first three terms in a GP is 38.Their product is 1728.Find the values of the three terms.
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   r  = 12%2Fa.                   (4)

Now, in equation (1) replace the term  ar  by 12, based on (3).  You will get

   a + 12 + ar^2 =  38,   which implies

   a + ar^2 = 26.              (5)

Next, substitute  r = 12%2Fa  into equation (5), replacing "r" there.  You will get

   a + a%2A%28144%2Fa%5E2%29 = 26,   or

   a + 144%2Fa = 26.

Multiply by "a" both sides and simplify

   a^2 - 26a + 144 = 0,

   %28a-13%29%5E2 - 169 + 144 = 0

   %28a-13%29%5E2 = 25

   a - 13 = +/- sqrt%2825%29 = +/- 5.

Thus two solutions for "a" are  a = 13 + 5 = 18  or  a = 13 - 5 = 8.

If  a =  8, then from (4)  r = 12%2F8 = 3%2F2.

If  a = 18, then from (4)  r = 12%2F18 = 2%2F3.

   

In the first case, if a = 8,  then the three terms are  8, 8%2A%283%2F2%29 = 12  and  8%2A%283%2F2%29%5E2 = 18.

   In this case, the sum of terms is  8 + 12 + 18 = 38, so this solution does work.

In the second case, if a = 18,  then the three terms are  18, 18%2A%282%2F3%29 = 12  and  18%2A%282%2F3%29%5E2 = 8.

   In this case, the sum of terms is  18 + 12 + 8 = 38, so this solution does work, too.

ANSWER.  The problem has two solution:  

        a)  first term is 18;  the common difference is 2%2F3  and the progression is  18, 12, 8.

        b)  first term is  8;  the common difference is 3%2F2  and the progression is   8, 12, 18.

4 0
3 years ago
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