A bank credit card charges interest at the rate of 23% per year, compounded monthly. If a senior in college charges $1,700 to pay for college expenses, and intends to pay it in one year, what will she have to pay?
2,134.97
monthly rate = .23/12 = .0191666..
Since it is a credit card, I am assuming that you want equal monthly payments
let that payment be P
P( 1 - 1.01916666..^-12)/.019666.. = 1700
p(10.6296677) = 1700
P = $159.93
I think the question is asking what she would pay at the end of the year. I tried $159.93 and it was not correct.
your finding the interest... but your looking for that in the year to pay off her credit card debt it would cost 2,091
To calculate the total amount that the senior in college will have to pay, we need to determine the interest accrued on the $1,700 principal amount over one year.
Given that the interest is compounded monthly at a rate of 23% per year, we can break down the annual interest rate into a monthly rate.
Step 1: Calculate the monthly rate
To find the monthly interest rate, we divide the annual interest rate by 12 (since there are 12 months in a year).
Monthly Interest Rate = Annual Interest Rate / 12
= 23% / 12
= 0.23 / 12
= 0.0191667 (rounded to 7 decimal places)
Step 2: Determine the total number of compounding periods
Since the interest is compounded monthly for one year, the total number of compounding periods is 12.
Step 3: Calculate the future value
We can use the compound interest formula to calculate the future value (amount to be paid) after one year:
Future Value = Principal * (1 + Monthly Interest Rate)^(Number of Compounding Periods)
= $1,700 * (1 + 0.0191667)^12
Calculating this expression will give us the total amount the senior in college will have to pay.
Let's do the math:
Future Value = $1,700 * (1 + 0.0191667)^12
= $1,700 * (1.0191667)^12
≈ $1,893.17
Therefore, the senior in college will have to pay approximately $1,893.17 at the end of one year to cover the charges and the accrued interest.