Question

Use PMT=to determine the regular payment amount, rounded to the nearest dollar Your credit card has a balance of $4700 and an annual interest rate of 12% You decide to pay off the balance-M]over two years. If there are no further purchases charged to the card,a. How much must you pay each month?b. How much total interest will you pay?a. The monthly payments are approximately $(Do not round until the final answer. Then round to the nearest dollar as needed.)b. The total interest paid over 2 years is approximately $(Round to the nearest dollar as needed)

Answer 1

To calculate the monthly payment for a $4700 credit card debt at a 12% annual interest rate paid off over two years, the PMT formula is used. After computing the monthly payment, multiply it by 24 to get the total amount paid and subtract the original debt to find the total interest paid.

Step-by-step explanation:

To determine the monthly payment needed to pay off a credit card debt with a balance of $4700 and an annual interest rate of 12% over two years, we use the PMT formula, which calculates the payment for a loan based on constant payments and a constant interest rate. The formula for calculating the monthly payment (PMT) is:

PMT = [P x i] / [1 - (1 + i)^(-n)]

Where:

• P represents the principal amount ($4700)
• i represents the monthly interest rate (annual rate divided by 12 months)
• n represents the total number of payments (2 years times 12 months per year)

First, we convert the annual interest rate to a monthly rate:
12% annual rate = 0.12 annual rate
Monthly rate = 0.12 / 12 = 0.01

Next, we calculate 'n', the total number of monthly payments:
2 years x 12 months/year = 24 months

Now we have all the variables needed to plug into the PMT formula:

PMT = [4700 x 0.01] / [1 - (1 + 0.01)^(-24)]

Calculating the above will give us the regular monthly payment. After finding PMT, we can multiply the monthly payment by 24 months to determine the total amount paid. Then, subtract the original debt of $4700 to find out the total interest paid over 2 years.

Answer 2

Given

Credit card has a balance of $4700

An annual interest rate of 12%

Find

a) How much must you pay each month?

b) How much total interest will you pay?

Explanation

a) Here we use PMT ,

`(P*((r)/(n)))/(1-(1+(r)/(n))^(-n* t))`

here P = $4700

r = 12%

now , substitute the values ,

`\begin{gathered} (4700*((12\%)/(12)))/([1-(1+(12\%)/(12))^(-12*2)]) \\ \\ (4700*(1\%))/([1-(1+1\%)^(-24)]) \\ \\ (47)/(1-0.78756613) \\ \\ (47)/(0.21243387) \\ \\ 221.245322132\approx221.25 \end{gathered}`

b) Total interest paid over 2 years = (monthly payment * total number of months in a year*time period ) - current balance of credit card

so ,

`\begin{gathered} 221.25*12*2-4700 \\ 5310-4700 \\ 610 \end{gathered}`

Final Answer

Hence ,

a) The monthly payments are approximately $ 221.25

b) The total interest paid over 2 years is $610