Answer:
Hi
Step-by-step explanation:
Certainly! Let's break down the questions one by one:
**a. Calculate your monthly payments:**
To calculate the monthly payments, we can use the credit card interest formula. The formula for calculating the monthly payment (PMT) required to pay off a loan or credit card balance over a fixed period of time is:
\[ \text{PMT} = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \]
Where:
- \(P\) is the initial balance (in this case, $6200).
- \(r\) is the monthly interest rate (APR divided by 12 and expressed as a decimal).
- \(n\) is the total number of payments (number of years multiplied by 12).
Given that the APR is 16%, let's calculate the monthly interest rate:
\[ r = \frac{16\%}{12} = 0.0133 \]
Now, plug in the values:
\[ \text{PMT} = \frac{6200 \cdot 0.0133 \cdot (1 + 0.0133)^{5 \cdot 12}}{(1 + 0.0133)^{5 \cdot 12} - 1} \]
Using a calculator, the monthly payment (\(\text{PMT}\)) comes out to approximately **$146.66**.
**b. When the card is paid off, how much will you have paid since January 1?**
The total amount paid can be calculated by multiplying the monthly payment by the total number of payments:
\[ \text{Total Amount Paid} = \text{PMT} \cdot (5 \cdot 12) \]
Substitute the value of \(\text{PMT}\):
\[ \text{Total Amount Paid} = 146.66 \cdot 60 = \$8799.60 \]
Therefore, you will have paid approximately **$8799.60** since January 1.
**c. What percentage of your total payment (part b) is interest?**
To find the interest paid, subtract the initial balance from the total amount paid:
\[ \text{Interest Paid} = \text{Total Amount Paid} - P = 8799.60 - 6200 = \$2599.60 \]
Now calculate the percentage of interest relative to the total payment:
\[ \text{Interest Percentage} = \frac{\text{Interest Paid}}{\text{Total Amount Paid}} \cdot 100 \]
Substitute the values:
\[ \text{Interest Percentage} = \frac{2599.60}{8799.60} \cdot 100 \approx 29.54\% \]
Approximately **29.54%** of your total payment is interest.
Remember that these calculations assume no additional charges or changes in the balance during the repayment period. Actual results may vary based on the specific terms of your credit card agreement.
Kaynak: Bing ile konuĹźma, 01.04.2024
(1) Credit Card Monthly Payment Calculator - Cardratings.com. https://www.cardratings.com/monthly-payment-calculator.html.
(2) Credit Card Interest Calculator - NerdWallet. https://www.nerdwallet.com/article/credit-cards/credit-card-interest-calculator.
(3) Monthly Credit Card Interest Calculator - Cardratings.com. https://www.cardratings.com/credit-card-interest-calculator.html.
(4) Credit Card Calculator – Repayment and Interest Calculator | Uswitch. https://www.uswitch.com/credit-cards/calculator/.
(5) Credit Card Calculator. https://www.calculator.net/credit-card-calculator.html.
(6) Credit Card Interest Calculator. https://www.omnicalculator.com/finance/credit-card-interest.
(7) How Is Your Credit Card Interest Calculated? - LendingTree. https://www.lendingtree.com/credit-cards/articles/calculate-interest/.
