A bank credit card charges interest at the rate of 20% per year, compounded monthly. If a senior in college charges $1,300 to pay for college expenses, and intends to pay it in one year, what will he have to pay? (Round your answer to the nearest cent.)

0.20 / 12 = 0.01666666 per month

1300 * (1.01666666)^12
= 1300 * 1.219391
= 1585.21

Oh, college expenses, they really know how to add up, don't they? Well, let's do some math and see what we come up with!

So, we have a bank credit card that charges a delightful 20% interest per year, compounded monthly. Now, since it's compounded monthly, we need to convert that annual interest rate into a monthly rate.

To find the monthly interest rate, we divide the annual rate by 12: 20% / 12 = 1.67% (approximately).

Now, let's calculate the total amount our dear senior will have to pay back at the end of one year.

The formula for compound interest is A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal amount (initial amount), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the initial amount charged is $1,300, the interest rate is 1.67% (or 0.0167 in decimal form), it's compounded monthly (so n = 12), and the time period is one year (so t = 1).

Plugging in the values and doing some number crunching, we get:

A = 1300(1 + 0.0167/12)^(12*1)

Calculating this, we find that A is approximately $1,376.04.

So, our dear senior will have to pay back approximately $1,376.04 to cover those college expenses and interest. Better start saving up those pennies!

To calculate the amount the senior in college will have to pay after one year, we will use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:
A = the final amount
P = the principal amount (initial balance)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

Given:
P = $1,300
r = 20% = 0.20 (as a decimal)
n = 12 (compounded monthly)
t = 1

Plugging these values into the formula:

A = 1300(1 + 0.20/12)^(12*1)

Now, let's calculate step-by-step:

A = 1300(1 + 0.016666667)^(12)

1 + 0.016666667 = 1.016666667

A = 1300(1.016666667)^(12)

Now, let's use a calculator to calculate (1.016666667)^(12):

(1.016666667)^(12) = 1.195618858

A = 1300(1.195618858)

Now, multiply:

A = $1,554.40

Therefore, the senior in college will have to pay approximately $1,554.40 after one year.

To calculate the total amount the senior in college will have to pay, we need to consider the principal amount (the initial $1,300) and the interest added over the course of the year.

Given that the interest is compounded monthly at a rate of 20% per year, we first need to convert the annual interest rate to a monthly interest rate.

Step 1: Convert the annual interest rate to a monthly interest rate.
To calculate the monthly interest rate, divide the annual interest rate by 12 (the number of months in a year).
Monthly interest rate = (Annual interest rate) / 12

In this case:
Monthly interest rate = 20% / 12 = 0.20 / 12 = 0.0167 (rounded to 4 decimal places)

Step 2: Calculate the interest for each month and add it to the outstanding balance.
To calculate the interest for each month, multiply the outstanding balance at the start of the month by the monthly interest rate.
Interest for the month = (Outstanding balance at the start of the month) * (Monthly interest rate)

At the end of each month, the outstanding balance is the sum of the previous balance and the interest for the month.

Step 3: Calculate the total payment at the end of the year.
At the end of the year, the total payment will be the sum of the initial principal amount and the cumulative interest over the year.

Now, let's calculate the total payment:

Month 1:
Outstanding balance = $1,300 + ($1,300 * 0.0167) = $1,322.10

Month 2:
Outstanding balance = $1,322.10 + ($1,322.10 * 0.0167) = $1,344.56

Month 3:
Outstanding balance = $1,344.56 + ($1,344.56 * 0.0167) = $1,367.38

...

Month 12 (end of the year):
Outstanding balance = $1,448.42

Thus, the total payment at the end of the year will be $1,448.42 (rounded to the nearest cent).