Question

A bank credit card charges interest at the rate of 24% per year, compounded monthly. If a senior in college charges $1,500 to pay for college expenses, and intends to pay it in one ye

what will he have to pay? (Round your answer to the nearest cent.)

$

Answer 1

The student will have to pay $1,902.36 after one year on a $1,500 charge with a 24% annual interest rate compounded monthly.

Step-by-step explanation:

To calculate the amount a senior in college will need to pay back after one year on a $1,500 charge with an interest rate of 24% per year compounded monthly, we use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($1,500), r is the annual interest rate (24%), n is the number of times that interest is compounded per year (monthly compounding means n = 12), and t is the time the money is invested or borrowed for in years (t = 1).

First, convert the annual rate to a monthly rate by dividing by 12: r/n = 24%/12 = 2% per month. Then convert the percentage to a decimal for calculation: 2% = 0.02.

Now apply the formula:
A = $1,500(1 + 0.02)^12
A = $1,500(1.02)^12
A = $1,500(1.26824)
A = $1,902.36 (rounded to the nearest cent).
So, the student will have to pay back $1,902.36 after one year.

Answer 2

Answer: 1902.36

Step-by-step explanation:

When interest is compounded monthly , the formula to find the accumulated amount is

`A=P(1+(r)/(12))^(12t)` , where P = principal value , r = rate of interest , t = time.

As per given,

r= 24% = 0.24

P= $1500

t= 1 year

Put all value in formula , we get

`A= 1500(1+(0.24)/(12))^(12* 1)\\\\=1500(1+0.02)^(12)\\\\=1500(1.02)^(12)\\\\=1500(1.26824179456)\approx1902.36`

Hence, he need to pay $1902.36.