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xxTIMURxx [149]
3 years ago
15

Credit card A has an APR of 26.2% and an annual fee of $30, while credit card B has anAPR of 27.1% and no annual fee. ALl else b

eing equal,at about what balance will the cards offer the same deal over the course of a year?(Assume all interest is compounded monthly.)
A. $261.78
B. $2617.85
C.$26,178.46
D.$26.18
Mathematics
2 answers:
butalik [34]3 years ago
5 0
Taking the quiz now. 
The answer is $2617.85.
Ipatiy [6.2K]3 years ago
3 0

Let the required balance be x.

Thus, for Card A, which has an APR of 26.2% and an annual fee of $30, the amount after a year when compounded monthly will be:

Amount_A=30+(1+\frac{0.262}{12})^{12}x........(Equation 1)

Likewise, for Card B, which has an APR of 27.1% and no annual fee, the amount after a year when compounded monthly will be:

Amount_B=0+(1+\frac{0.271}{12})^{12}x=(1+\frac{0.271}{12})^{12}x....(Equation 2)

Therefore, all else being equal, the balance, x, at which the cards offer the same deal over the course of a year can be found by equating the equations 1 and 2 and solving for x.

Thus we have:

30+(1+\frac{0.262}{12})^{12}x=(1+\frac{0.271}{12})^{12}x

30+(1.0218)^{12}x=(1.0226)^{12}x

Simplification gives us:

(1.0226)^{12}x-(1.0218)^{12}x=30

0.0122x=30

\therefore x\approx2459.02 dollars

This is the closest to the second option. Thus, option B is the correct option.

<u>Important Note:</u> If we do not round off the intermediate steps and calculate it directly using a calculator then we will get the exact answer of option B which is: $2617.85.


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