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James has a balance of $1700 on a credit card with an APR of 18.7%, compounded monthly. About how much will he save in interest over the course of a year if he transfers his balance to a credit card with an APR of 12.5%, compounded monthly? (Assume that James will make no payments or new purchases during the year, and ignore any possible late payment fees.)

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sqdancefan

Answer:

  $121.51

Step-by-step explanation:

At 18.7%, the monthly multiplier is 1+.187/12, so for the year, James' balance is multiplied by (1+.187/12)^12 ≈ 1.2038899

At 12.5%, the monthly multiplier is 1+.125/12, so for the year, James' balance is multiplied by (1+.125/12)^12 ≈ 1.1324161

The difference in these multipliers is ...

  1.2038899 -1.13241605 = 0.0714739

so James' savings is ...

  $1700 × 0.0714739 ≈ $121.51

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