+16 Cynthia had a credit card with a 17% APR and a $3,265 balance. She had budgeted to have the credit card paid off in 24 months. But after missing a single monthly payment, Cynthia’s credit card company has increased her interest rate to 21%. How much extra will Cynthia have to pay in finance charges (interest) because of the increase in her APR if she still pays off the credit card in 24 months? please show work so i can see how you got the answer im so confused..
+118667 Cynthia had a credit card with a 17% APR and a $3,265 balance. She had budgeted to have the credit card paid off in 24 months. But after missing a single monthly payment, Cynthia’s credit card company has increased her interest rate to 21%. How much extra will Cynthia have to pay in finance charges (interest) because of the increase in her APR if she still pays off the credit card in 24 months? please show work so i can see how you got the answer im so confused..
The meaning of this question is not particularly clear.
This is my interpretation.
What is the difference between paying it off over 24months at 17% compared to paying it off over 24 months at 21%p.a.
It is the present value of an ordinary annuity problem.
We know what the present value is so I need to make C the subject of the formula
\(PV=C*\left[\frac{1-(1+i)^{-n}}{i} \right]\\~\\ Let \;\;T=1+i\\~\\ PV=C*\left[\frac{1-T^{-n}}{i} \right]\\~\\ PV*\left[\frac{i} {1-T^{-n}} \right]=C\\~\\ C=PV*\left[\frac{i} {1-T^{-n}} \right]\\ \)
$3,265 over 24months at 17%
PV=3265, n=24 i=0.17/12 = 0.014166666... T=1.01416666666...
3265(0.014166666666/(1-1.014166666666^-24)) = 161.428992237891374646345210584850429611154
Monthly payments will be $161.43
$3,265 over 24months at 21%
PV=3265, n=24 i=0.21/12 =0.0175 T=1.0175
3265(0.0175/(1-1.0175^-24)) = 167.7741503813724470006323048290321
Monthly payments will be $167.77
The difference between these two will all be added interest charges.
167.77-161.43 = $ 6.34 per month
6.34*24 = $152.16 over the two years
