Question

Monica has recently inherited $7700, which she wants to deposit into a CD accountShe has determined that her two best bets are an account that compounds annually at an annual rate of 4.9% ( Account 1) and an account that compounds continuously at an annual rate of 5.1% (Account 2) Step 2 of 2: How much would Monica's balance be from Account 2 over 3.5 years? Round to two decimal places

Answer 1

Monica's balance from Account 2 over 3.5 years would be approximately $9196.18.

Step-by-step explanation:

To determine Monica's balance from Account 2 over 3.5 years, we can use the formula for compound interest with continuous compounding:

A = Pe^(rt)

Where:

• A is the amount after time t
• P is the principal amount
• e is the mathematical constant approximately equal to 2.71828
• r is the annual interest rate
• t is the time in years

In this case, Monica deposited $7700, so P = $7700. The annual interest rate is 5.1%, so r = 0.051. The time period is 3.5 years, so t = 3.5.

Substituting these values into the formula, we have:

A = $7700 * e^(0.051 * 3.5)

Using a calculator, we can calculate the value of e^(0.051 * 3.5) to be approximately 1.194. Multiplying this by the principal amount, we get:

A = $7700 * 1.194 = $9196.18

Therefore, Monica's balance from Account 2 over 3.5 years would be approximately $9196.18.