cynthia had a credit card with a 17% apr and a $3,265 balance. she had budgeted to have the credit card paid…

Answer:

b. $272.08

Explanation:

Step1: Calculate monthly rate for 17% APR

Monthly rate $r_1=\frac{0.17}{12}$

Step2: Calculate monthly payment for 17% APR

Using the formula for the present - value of an ordinary annuity $PV = PMT\times\frac{1-(1 + r)^{-n}}{r}$, where $PV = 3265$, $n = 24$, and $r=r_1$. $3265=PMT_1\times\frac{1-(1+\frac{0.17}{12})^{-24}}{\frac{0.17}{12}}$ $PMT_1=\frac{3265\times\frac{0.17}{12}}{1-(1+\frac{0.17}{12})^{-24}}\approx159.47$ Total payment $= 159.47\times24 = 3827.28$ Interest paid $I_1=3827.28 - 3265=562.28$

Step3: Calculate monthly rate for 21% APR

Monthly rate $r_2=\frac{0.21}{12}$

Step4: Calculate monthly payment for 21% APR

Using the present - value of an ordinary annuity formula with $PV = 3265$, $n = 24$, and $r = r_2$. $3265=PMT_2\times\frac{1-(1+\frac{0.21}{12})^{-24}}{\frac{0.21}{12}}$ $PMT_2=\frac{3265\times\frac{0.21}{12}}{1-(1+\frac{0.21}{12})^{-24}}\approx170.64$ Total payment $=170.64\times24 = 4095.36$ Interest paid $I_2=4095.36 - 3265 = 830.36$

Step5: Calculate extra interest

Extra interest $=I_2 - I_1=830.36 - 562.28 = 272.08$