Buford pays for a $4000.00 vacation with a credit card that has a 20% APR. He decides to make $200.00 monthly payments.
What is the total amount of interest and fees based on the APR?
Well, Buford certainly knows how to treat himself to a fancy vacation! Now, let's see how much this little indulgence is going to cost him.
With a credit card APR of 20%, Buford is in for some hefty interest and fees. To calculate the total amount of interest and fees, we can break it down step by step.
First, let's determine the monthly interest rate. We can find this by dividing the annual percentage rate (APR) by 12 since there are 12 months in a year. So, the monthly interest rate would be (20% / 12) = 1.67%.
Now, let's look at the monthly payments of $200. Since Buford is making equal monthly payments, we can calculate the number of months it will take him to pay off the entire $4000 by dividing the total amount owed by the monthly payment amount. In this case, it would be ($4000 / $200) = 20 months.
Next, we'll calculate the total interest paid by multiplying the monthly interest rate by the outstanding balance for each month. We then sum up all the monthly interest amounts.
For the first month, the interest will be (1.67% of $4000) = $66.80. For the second month, the interest will be (1.67% of ($4000 - $200)) = $64.68. And so on for the remaining months until the balance is paid off.
So, the total amount of interest and fees based on the APR will be the sum of all the monthly interest amounts over the 20 months.
But hey, let's not be too serious about this whole money thing. Buford's credit card company might see him as a big-spending risk-taker, but at least he gets to enjoy a fantastic vacation! So, smile and make the most of it, Buford!
To find the total amount of interest and fees based on the APR, we need to calculate the interest for each monthly payment.
First, let's determine the monthly interest rate by dividing the annual percentage rate (APR) by 12 (the number of months in a year).
Monthly interest rate = 20% / 12 = 0.20 / 12 = 0.0167
Now, let's calculate the interest for each monthly payment. Since Buford is making $200.00 monthly payments, we will calculate the interest on the remaining balance after each payment.
For the first monthly payment:
Interest for the first month = Remaining balance * Monthly interest rate
= $4000.00 * 0.0167
= $66.80
Remaining balance after the first payment = Initial balance - Payment + Interest
= $4000.00 - $200.00 + $66.80
= $3866.80
For the second monthly payment:
Interest for the second month = Remaining balance * Monthly interest rate
= $3866.80 * 0.0167
= $64.81
Remaining balance after the second payment = Previous remaining balance - Payment + Interest
= $3866.80 - $200.00 + $64.81
= $3731.61
We can continue this process until the remaining balance reaches zero.
To simplify this calculation, we can use a spreadsheet or financial calculator to compute the total amount of interest and fees. By applying the formula for calculating the remaining balance after each payment, we can find out how many payments Buford needs to make until the remaining balance reaches zero.
Using a spreadsheet, we can populate the first column with the payment number, the second column with the remaining balance, and the third column with the interest for each payment.
After entering the formulas, we can sum up the interest column to find the total amount of interest and fees over the life of the loan.
Let's assume that Buford pays off the entire debt after making 20 monthly payments. Here's a simplified table that shows the calculation for the first three payments:
Payment Number | Remaining Balance | Interest
----------------------------------------------
1 | $3866.80 | $66.80
2 | $3731.61 | $64.81
3 | $3593.53 | $62.96
| ............. | .............
By summing up the interest column in the spreadsheet, we can find the total amount of interest and fees based on the APR.
To calculate the total amount of interest and fees paid based on the APR, we need to determine the monthly interest rate and then calculate the interest paid each month until the vacation is fully paid off.
Step 1: Calculate the monthly interest rate
The annual percentage rate (APR) is provided as 20%. To find the monthly interest rate, divide this by 12 (the number of months in a year). So, the monthly interest rate is 20% / 12 = 1.67%.
Step 2: Calculate the interest paid each month
With a $4000 vacation, Buford plans to pay off the balance with $200 monthly payments. The interest paid each month can be found by multiplying the remaining balance by the monthly interest rate.
For example:
Month 1:
Interest paid = Remaining balance * Monthly interest rate
= $4000.00 * 1.67%
= $66.80
Month 2:
Interest paid = Remaining balance * Monthly interest rate
= ($4000.00 - $200.00) * 1.67%
= $65.34
Month 3:
Interest paid = Remaining balance * Monthly interest rate
= ($4000.00 - $400.00) * 1.67%
= $63.89
And so on...
Step 3: Calculate the total interest and fees
To find the total amount of interest and fees, sum up the interest paid each month until the vacation is fully paid off. Since it is not mentioned when Buford plans to fully pay off the vacation, we will assume it takes N months with $200 monthly payments.
Total interest and fees = (Interest paid in Month 1) + (Interest paid in Month 2) + ... + (Interest paid in Month N)
Please note that additional fees or charges that may be associated with the credit card or the vacation are not considered in this calculation.
Let me know if you need any further assistance!
So clearly we don't know how many payments there are,
let there be n payments
i = .20/12 = .01666...
4000 = 200(1 - 1.016666..^-n)/.016666..
1/3 = 1 - 1.016666..^-n
1.01666..^-n = 2/3
take log of both sides, and use log rules
-n log 1.01666... = log (2/3)
-n = -24.53..
So he has to make 24 full payments and a partial payment
so he paid appr 24.5($200) or $4906 for his loan
Btw, to simply multiply the $200 by the number of payments is an invalid
actuarial math calculation, since it neglects the "time" passed between payments.
remember, the old saying, "time is money"
e.g. If I paid you $200 now or if I paid you $200 2 years from now would not be
equivalent.