Michael has a credit card with a credit limit of €1000 - Leaving Cert Mathematics - Question b - 2013

To calculate the total amount owed after 15 months, we can use the formula for compound interest:

$F = P(1 + i)^n$

Where:

• $F$ is the future value (amount owed after 15 months)
• $P$ is the principal amount (€800)
• $i$ is the monthly interest rate (1.5% = 0.015)
• $n$ is the number of months (15)

Substituting the values:

$F = 800(1 + 0.015)^{15}$

Calculating:

$F = 800(1.015)^{15}$

Now calculating the exponent:

F ≈ €996.79$$ After 15 months, Michael will owe approximately €996.79. Since this is less than €1000, we now check for month 16 to determine if he exceeds the credit limit. In month 16: $$F = 996.79(1 + 0.015) = 996.79(1.015) ≈ €1011.50$$ Thus, Michael will exceed his credit limit after 15 months.