A bank credit card charges interest at the rate of 24% per year, compounded monthly. If a senior in college charges $1,100 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.)
Silly and unreasonable question. Who would let a 24% credit card go for a whole year without any payment, and what company would not let you make payments ????
anywhoo...
i = .24/12 = .02
n = 12
amount = 1100(1.02)^12 = $1395.07
Oh, college expenses! The only thing scarier than clowns. But let's crunch some numbers and see what we get!
So, we have a senior in college charging $1,100 to the credit card. The interest rate is 24% per year, compounded monthly. This means that the interest is added to the balance every month.
To find out what he'll have to pay, we need to calculate the total amount he owes after one year. Here's how we can do it:
First, we need to find the monthly interest rate. Since it's 24% per year, we divide that by 12 (for the 12 months in a year), and we get 2% per month (0.02 as a decimal).
Next, we need to calculate the total balance after one year. To do this, we use the formula for compound interest:
Total balance = Principal * (1 + monthly interest rate)^(number of months).
In this case, the principal is $1,100, the monthly interest rate is 0.02, and the number of months is 12.
Plugging in these values, we get:
Total balance = $1,100 * (1 + 0.02)^12.
After doing the math (and keeping it as precise as possible), the total balance comes out to be approximately $1,297.88.
So, it looks like our senior will have to pay about $1,297.88 in one year to cover those college expenses.
Hope this helps! Just remember, humor is always compound-interesting. But financial decisions? Not-so-funny.
To find out how much the senior in college will have to pay after one year, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (initial charge)
r = annual interest rate (in decimal form)
n = number of times compounded per year
t = number of years
In this case,
P = $1,100
r = 24% per year = 0.24 in decimal form
n = 12 (compounded monthly)
t = 1 year
Plugging the values into the formula, we get:
A = 1100(1 + 0.24/12)^(12*1)
Simplifying the expression inside the parentheses:
A = 1100(1 + 0.02)^(12*1)
A = 1100(1.02)^12
Calculating (1.02)^12:
A = 1100(1.268241794)
A = $1,395.07
Therefore, the senior in college will have to pay approximately $1,395.07.
To find out how much the senior in college will have to pay, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
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 = time in years
Given information:
P = $1,100
r = 24% = 0.24 (as a decimal)
n = 12 (compounded monthly)
t = 1 year
Now let's plug in the values into the formula:
A = 1100(1 + 0.24/12)^(12*1)
A = 1100(1 + 0.02)^(12)
Calculating the inside of the parentheses first:
A = 1100(1.02)^(12)
A = 1100 * 1.268242
A ≈ $1,395.07
Therefore, the senior in college will have to pay approximately $1,395.07.