Question

Lois has a balance of $970 on a credit card with an APR of 24.2%, compounded monthly. About how much will she save in interest over the course of the year if she transfers her balance to a credit card with an APR of 10.8%, compounded monthly?

Answer 1

Answer:

$152.51

Explanation:

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Answer 2

Answer:

Lois will save $152.51 when she wil transfer her balance.

Explanation:

Amount to be paid in 1 year for original credit card is given as

$P_1^{'}=P*(1+r_1)^t$

Here $P^{'}_1$ is the amount to be paid after P is the balance which is 970, $r_1$ is the APR for first credit card which is 24.2% and t is compounding frequency which is 12 so

$P_1^{'}=P*(1+r_1)^t\\P_1^{'}=970*(1+\dfrac{24.2}{12}\%)^{12}\\P_1^{'}=970*(1.0207)^{12}\\P_1^{'}=970*1.2707\\P_1^{'}=\ 1232.61$

Similarly for the second one the values are calculated as

$P_2^{'}=P*(1+r_2)^t\\P_2^{'}=970*(1+\dfrac{10.8}{12}\%)^{12}\\P_2^{'}=970*(1.108)^{12}\\P_2^{'}=970*1.1135\\P_2^{'}=\ 1080.10$

The differnce of the two values is calculated as

$P_1'-P_2'=1232.61-1080.10\\Difference=\ 152.51$

The difference is $152.51 which she could save.