8 Finance A credit card company charges interest at \( 2 \% \) per month on any outstanding balance. A balance of \( \$ 1500 \) is left unpaid. Work out the balance after \( \begin{array}{lll}\text { a } 1 \text { month } & \text { b } 6 \text { months } & \text { c } 1 \text { year. }\end{array} \)

The interest is compounded monthly. To calculate the balance after n months, we use the formula:   Final Balance = Principal × (1 + Interest Rate)^n Here, the principal is $1500 and the monthly interest rate is 2% or 0.02. a) After 1 month (n = 1):   Final Balance = 1500 × (1 + 0.02)¹ = 1500 × 1.02 = $1530 b) After 6 months (n = 6):   Final Balance = 1500 × (1.02)⁶   First, calculate 1.02⁶ ≈ 1.12616 (rounded to five decimal places)   Final Balance ≈ 1500 × 1.12616 ≈ $1689.24 c) After 1 year (12 months, n = 12):   Final Balance = 1500 × (1.02)¹²   Calculate 1.02¹² ≈ 1.26824 (rounded to five decimal places)   Final Balance ≈ 1500 × 1.26824 ≈ $1902.36 Thus, the balance is approximately:  a) $1530 after 1 month,  b) $1689.24 after 6 months, and  c) $1902.36 after 1 year.