You owe $1,350.00 on a credit card with a 14.25% APR. You pay $300.00 at the beginning of the month. How much interest do you save by paying at the beginning of the month versus at the end of the month?

second part:
Imagine you put the $300 in a savings account earning 3.0% APR instead of using it to pay down your credit card as in Problem 3. What is the difference between the interest your savings account would earn that month vs. the interest that would accrue on your credit card that month if you didn't use the $300 to pay it down?

I am confused please help

1. 1350 * (14.25%/12) = 16.03

1050 * (14.25%/12) = 12.47
16.03 - 12.47 = 3.56

2. 1350 * (14.25%/12) = 16.03 interest at end of month credit card
300 * (3%/12) = 0.75 interest at end of month savings account
16.03 - 0.75 = 15.28

Well, let's break it down and have some fun with the math, shall we?

First part: How much interest do you save by paying at the beginning of the month versus at the end of the month?

Well, by paying $300 at the beginning of the month, you're reducing your outstanding balance, which means less money for the credit card company to charge interest on. So, to calculate the interest savings, we need to find the interest charged for the whole month with the original balance of $1,350.00 and subtract the interest charged with the reduced balance after your payment.

For simplicity, let's assume there are 30 days in the month. The interest charged at 14.25% APR for a whole month on $1,350.00 would be:

Interest = ($1,350.00 * 0.1425)/365 * 30

And after paying $300, the new balance would be $1,050.00. So, the interest charged at 14.25% APR for a whole month on $1,050.00 would be:

Interest = ($1,050.00 * 0.1425)/365 * 30

To find the interest savings, we can subtract the second interest charge from the first. But hey, don't worry, I'll do the math for you:

Interest savings = (Interest with original balance) - (Interest with reduced balance)

See? Easy-peasy! Well, kinda.

Second part: The difference between the interest your savings account would earn and the interest that would accrue on your credit card if you didn't use the $300 to pay it down.

Now, let's imagine you didn't use that $300 to pay down your credit card but put it in a savings account earning 3.0% APR instead. This means you'd be earning interest on that money instead of paying interest on your credit card. Awesome, right?

To find the difference in interest earned, we need to calculate the interest earned in the savings account and subtract it from the interest charged on the credit card.

Interest earned in the savings account = ($300.00 * 0.03)/365 * 30

And we know the interest charged on the credit card with the reduced balance is:

Interest charged on credit card = (Balance after $300 payment * 0.1425)/365 * 30

To find the difference, we simply subtract the interest charged on the credit card from the interest earned in the savings account.

Difference = Interest earned in savings account - Interest charged on credit card

There you have it! The difference in interest earned on your savings account and the interest charged on your credit card. I hope this helps clear up the confusion, or at least distract you with some clown math! Happy calculating!

To calculate the amount of interest saved by paying at the beginning of the month versus at the end of the month, we need to consider the average daily balance for the month.

Step 1: Calculate the average daily balance
To find the average daily balance, add the beginning balance and the ending balance for the month, and divide by 2.

Beginning balance: $1,350.00
Ending balance: $1,350.00 - $300.00 (payment) = $1,050.00

Average daily balance = (Beginning balance + Ending balance) / 2
Average daily balance = ($1,350.00 + $1,050.00) / 2
Average daily balance = $2,400.00 / 2
Average daily balance = $1,200.00

Step 2: Calculate the interest paid by paying at the beginning of the month
To calculate the interest paid, multiply the average daily balance by the monthly interest rate.

Monthly interest rate = APR / 12
Monthly interest rate = 14.25% / 12 = 0.011875

Interest paid by paying at the beginning of the month = Average daily balance x Monthly interest rate
Interest paid by paying at the beginning of the month = $1,200.00 x 0.011875
Interest paid by paying at the beginning of the month = $14.25

Step 3: Calculate the interest paid by paying at the end of the month
To calculate the interest paid, multiply the ending balance by the monthly interest rate.

Interest paid by paying at the end of the month = Ending balance x Monthly interest rate
Interest paid by paying at the end of the month = $1,050.00 x 0.011875
Interest paid by paying at the end of the month = $12.47

Step 4: Calculate the interest saved
To find the interest saved, subtract the interest paid by paying at the beginning of the month from the interest paid by paying at the end of the month.

Interest saved = Interest paid by paying at the end of the month - Interest paid by paying at the beginning of the month
Interest saved = $12.47 - $14.25
Interest saved = -$1.78

Therefore, by paying $300.00 at the beginning of the month, you actually save $1.78 in interest compared to paying at the end of the month.

Now let's move on to the second part of the question.

Assuming you put the $300.00 in a savings account earning a 3.0% APR:

Step 1: Calculate the monthly interest earned in the savings account
To calculate the monthly interest earned in the savings account, multiply the amount deposited ($300.00) by the monthly interest rate.

Monthly interest rate (savings account) = 3.0% / 12 = 0.0025

Interest earned in the savings account = Amount deposited x Monthly interest rate
Interest earned in the savings account = $300.00 x 0.0025
Interest earned in the savings account = $0.75

Step 2: Calculate the interest accruing on the credit card
To calculate the interest accruing on the credit card, multiply the ending balance ($1,350.00) by the monthly interest rate.

Interest accruing on the credit card = Ending balance x Monthly interest rate
Interest accruing on the credit card = $1,350.00 x 0.011875
Interest accruing on the credit card = $16.01

Step 3: Calculate the difference
To find the difference between the interest earned on the savings account and the interest accruing on the credit card, subtract the interest earned from the interest accrued.

Difference = Interest accruing on the credit card - Interest earned in the savings account
Difference = $16.01 - $0.75
Difference = $15.26

Therefore, if you didn't use the $300.00 to pay down your credit card debt and instead put it in a savings account earning 3.0% APR, the difference between the interest your savings account would earn and the interest that would accrue on your credit card that month is $15.26.

To calculate the interest saved by paying at the beginning of the month instead of the end, we need to understand a few concepts.

First, we'll calculate the interest charged for the month on the credit card balance. The APR (Annual Percentage Rate) is provided, which means it's the interest rate charged for a year. To find the monthly interest rate, we divide the APR by 12. In this case, the monthly interest rate is (14.25% / 12).

To find the interest charged for the month, we multiply the monthly interest rate by the outstanding balance. In this case, the outstanding balance is $1,350.00. Therefore, the monthly interest charged on the credit card is ($1,350.00 * (14.25% / 12)).

Now, let's calculate the interest saved by paying at the beginning of the month. If you pay $300.00 at the beginning, the remaining balance on the credit card is ($1,350.00 - $300.00).

To find the interest charged if paid at the end of the month, we multiply the remaining balance by the monthly interest rate. The remaining balance is ($1,350.00 - $300.00), and therefore, the interest charged when paid at the end of the month is (($1,350.00 - $300.00) * (14.25% / 12)).

To calculate the interest saved, we subtract the interest charged at the end of the month from the interest charged at the beginning of the month. This gives us the difference in interest saved by paying earlier.

Moving on to the second part:

If you put the $300.00 in a savings account earning a 3.0% APR, you can calculate the interest earned by multiplying it by the monthly interest rate. The monthly interest rate for the savings account would be (3.0% / 12).

Thus, to find the interest earned in the savings account, we multiply the $300.00 by (3.0% / 12). This will give us the amount of interest earned in the savings account for the month.

Finally, to calculate the difference between the interest earned in the savings account and the interest accrued on the credit card, we subtract the interest accrued on the credit card from the interest earned in the savings account.

I hope this explanation helps in understanding how to calculate the interest saved and the difference in interest between the savings account and the credit card.