Luke deposited $4000 into a savings account that earns 4.00% annually but is compounded 4 times per year. He plans to leave the funds in the accounts for 4.00 years.
However, at the end of 2.50 years, Luke has to withdraw $500. What amount will be in the account at the end of the original 4.00 years

We can solve this problem using the compound interest formula:

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

Where:
- $ A $ is the amount in the account after time $ t $,
- $ P $ is the principal (initial deposit),
- $ r $ is the annual interest rate (in decimal form),
- $ n $ is the number of times interest is compounded per year,
- $ t $ is the time the money is invested for (in years).

### Step 1: Calculate the amount after 2.50 years

First, we calculate the amount in the account after 2.50 years without considering the $500 withdrawal.

Given:
- $ P = 4000 $ (initial deposit),
- $ r = 0.04 $ (4% annual interest rate),
- $ n = 4 $ (quarterly compounding),
- $ t = 2.5 $ years.

Substitute these values into the compound interest formula:

\[
A = 4000 \left( 1 + \frac{0.04}{4} \right)^{4 \times 2.5}
\]

### Step 2: Subtract the $500 withdrawal

Once we calculate the amount after 2.5 years, we subtract the $500 that Luke withdrew.

### Step 3: Calculate the remaining balance after 4.00 years

After the withdrawal, the new principal becomes the balance at 2.50 years minus $500. We then use this new principal to calculate the amount at the end of the full 4.00 years, with the remaining 1.50 years of compounding.

Let me calculate this.After 2.50 years, the amount in the account is approximately **$4418.49**. After withdrawing $500, the new balance is **$3918.49**.

By the end of the original 4.00 years, the amount in the account will be approximately **$4159.55**.

Would you like more details on any of the steps? Here are 5 related questions for further understanding:

1. How does the frequency of compounding affect interest earned?
2. What would happen if Luke did not withdraw any money at all?
3. How would the result change if the interest rate increased to 5%?
4. Can you explain the difference between simple and compound interest?
5. How do you calculate continuous compounding?

**Tip:** The more frequently interest is compounded, the greater the amount of interest earned.

Luke deposited $4000 into a savings account that earns 4.00% annually but is compounded 4 times per year. He plans to leave the funds in the accounts for 4.00 years. However, at the end of 2.50 years, Luke has to withdraw $500. What amount will be in the account at the end of the original 4.00 years?

Learn how to calculate the compound interest on a savings account with quarterly compounding, including a withdrawal after 2.50 years. This step-by-step solution demonstrates the compound interest formula and shows how to adjust for a mid-period withdrawal. Suitable for students in Grades 10-12.

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