Let's break down this scenario step by step:

Information provided:

1. Initial Deposit (Principal): $24,000
2. Interest rate for the 10-year account: 5.0% compounded quarterly
3. Interest rate for simple savings account: 2.5% compounded daily
4. Withdrawal: $8,000 after 18 months
5. Time Period for Calculation: 18 months, with each month assumed to have 30 days.

We need to answer various questions about how much Emma's money will grow or change after 18 months of deposit and withdrawal. Let’s go step-by-step:

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1. Compound Interest Calculation for the 10-Year Account (Quarterly Compounding)

We will use the formula for compound interest, which is:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount after interest
• $P$ is the principal amount (initial deposit)
• $r$ is the annual interest rate (decimal form)
• $n$ is the number of times interest is compounded per year
• $t$ is the number of years the money is invested for

For this case:

• $P = 24,000$
• $r = 0.05$ (5%)
• $n = 4$ (since it's compounded quarterly)
• $t = 1.5$ years (18 months)

Step 1: Calculate the amount after 18 months with the 10-year account.

Let me do the calculation. Given values for compound interest calculation P = 24000 # Initial deposit r = 0.05 # Annual interest rate n = 4 # Compounded quarterly t = 1.5 # Time period in years (18 months)

Compound interest formula: A = P(1 + r/n)^(nt)

A = P * (1 + r / n) ** (n * t) A