Question

Piper invested $990 in an account paying an interest rate of 33 % compounded continuously. Sadie invested $990 in an account paying an interest rate of 3​ % compounded monthly. After 14 years, how much more money would piper have in her account than sadie, to the nearest dollar?

Answer 1

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.