Respuesta :
Hi there
We know that the formula of the present value of annuity ordinary is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value
PMT monthly payment
R interest rate
K compounded monthly 12 because the payment is monthly
N time
What we need from the formula above to find the monthly payment
So to find the monthly payment the formula
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
Another important things we need is how to find total payments and interest charge
To find total payments
Monthly payment×12
And to find interest charge
Total payments-present value
Now let's find interest charge for each credit card
Credit card A
The monthly payment is
PMT=563÷((1−(1+0.16÷12)^(
−12))÷(0.16÷12))=51.08
Total payments
51.08×12=612.96
interest charge
612.96−563=49.96
Credit card b
PMT=2,525÷((1−(1+0.21÷12)^(
−12))÷(0.21÷12))=235.11
Total payments
235.11×12=2,821.32
interest charge
2,821.32−2,525=296.32
Credit card c
PMT=972÷((1−(1+0.19÷12)^(
−12))÷(0.19÷12))=89.58
Total payments
89.58×12=1,074.96
interest charge
1,074.96−972=102.96
So total interest charge for all credit cards is
102.96+296.32+49.96
=449.24....final answer
It's c
Good luck!
We know that the formula of the present value of annuity ordinary is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value
PMT monthly payment
R interest rate
K compounded monthly 12 because the payment is monthly
N time
What we need from the formula above to find the monthly payment
So to find the monthly payment the formula
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
Another important things we need is how to find total payments and interest charge
To find total payments
Monthly payment×12
And to find interest charge
Total payments-present value
Now let's find interest charge for each credit card
Credit card A
The monthly payment is
PMT=563÷((1−(1+0.16÷12)^(
−12))÷(0.16÷12))=51.08
Total payments
51.08×12=612.96
interest charge
612.96−563=49.96
Credit card b
PMT=2,525÷((1−(1+0.21÷12)^(
−12))÷(0.21÷12))=235.11
Total payments
235.11×12=2,821.32
interest charge
2,821.32−2,525=296.32
Credit card c
PMT=972÷((1−(1+0.19÷12)^(
−12))÷(0.19÷12))=89.58
Total payments
89.58×12=1,074.96
interest charge
1,074.96−972=102.96
So total interest charge for all credit cards is
102.96+296.32+49.96
=449.24....final answer
It's c
Good luck!
The interest of credit cards A, B, and C is 49.96, 296.32, and 102.96 respectively. The total interest is 449.24 then the correct option is C.
What is APR?
APR on a credit card is the way of saying that the interest you are charged over a year is equal to roughly your balance.
Listed below are the balances and annual percentage rates for Jimmy's credit cards.
If Jimmy makes the same payment each month to pay off his entire credit card debt in the next 12 months.
We know that the formula
[tex]PV = \dfrac{PMT[1 - (1+\dfrac{r}{12})^{12n}]}{\dfrac{r}{12}}[/tex]
PV = present value
PMT = monthly payment
r = interest rate
n = time
For credit card A, we have
[tex]\begin{aligned} 563 &= \rm \dfrac{PMT[1 - (1+\dfrac{0.16}{12})^{12}]}{\dfrac{0.16}{12}}\\\\\rm PMT &= 51.08 \end{aligned}[/tex]
Total payment will be
→ 51.08 × 12 = 612.96
The interest charge will be
→ 612.96 − 563 = 49.96
For credit card B, we have
[tex]\begin{aligned} 2525&= \rm \dfrac{PMT[1 - (1+\dfrac{0.21}{12})^{12}]}{\dfrac{0.21}{12}}\\\\\rm PMT &= 235.11\end{aligned}[/tex]
Total payment will be
→ 235.11 × 12 = 2821.32
The interest charge will be
→ 2821.32 − 2525 = 296.32
For credit card C, we have
[tex]\begin{aligned} 972 &= \rm \dfrac{PMT[1 - (1+\dfrac{0.19}{12})^{12}]}{\dfrac{0.19}{12}}\\\\\rm PMT &= 89.58\end{aligned}[/tex]
Total payment will be
→ 89.58 × 12 = 1074.96
The interest charge will be
→ 1075.96 − 972 = 102.96
Then the total interest will be
Total interest = 102.96 + 296.32 + 49.96
Total interest = 449.24
More about the APR link is given below.
https://brainly.com/question/8846837
