Final answer:
To find out how much is owed on the credit card after 6 months without payment, calculate the compound interest on the initial $1800 balance with a 10% annual interest rate, compounded monthly. Use the formula A = P(1 + r/n)^(nt) to get the amount, which includes both the principal and the interest.
Step-by-step explanation:
To determine how much you will owe on your credit card after not making a payment for 6 months, we need to calculate the compound interest that has accrued on your balance. Given a 10% annual interest rate and an initial balance of $1800, the amount you owe can increase each month due to interest. Assuming there are no other fees for late payments or penalties besides the interest, we can calculate the new balance using the formula for compounded interest: A = P(1 + r/n)nt.
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount ($1800).
r = the annual interest rate (decimal) (10% = 0.10).
n = the number of times that interest is compounded per year (assuming monthly, n = 12).
t = the time the money is invested or borrowed for, in years (6 months = 0.5 years).
Plugging in the values: A = 1800(1 + 0.10/12)12*0.5. After doing the calculation, you will get the total amount owed after 6 months. This amount includes both the principal and the interest accrued over the 6 months.