Final answer:
Piper would have approximately $8,762.12 more in her account than Sadie after 14 years.
Step-by-step explanation:
To calculate the amount of money Piper would have in her account after 14 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount of money
- P is the initial amount of money
- r is the interest rate (as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
For Piper's account, the initial amount is $990, the interest rate is 33% (or 0.33), and the interest is compounded continuously, so n is infinity. Plugging in these values, we get:
A = 990 * e^(0.33 * 14) ≈ $11,889.95
For Sadie's account, the initial amount is also $990, the interest rate is 3% (or 0.03), and the interest is compounded monthly, so n is 12. Plugging in these values, we get:
A = 990 * (1 + 0.03/12)^(12 * 14) ≈ $3,127.83
To find the difference in the amounts, we subtract Sadie's amount from Piper's amount:
$11,889.95 - $3,127.83 ≈ $8,762.12
Therefore, Piper would have approximately $8,762.12 more in her account than Sadie after 14 years.