James invests $600,000 for 6 years at 3.5% interest rate. How much money would he earn at t he end of the period?

To calculate how much James would earn from his investment of $600,000 over 6 years at an interest rate of 3.5%, we need to specify the type of interest: **simple interest** or **compound interest**. I'll provide the formulas for both, assuming yearly compounding for the compound interest case.

### 1. **Simple Interest Formula**:
The formula for simple interest is:
\[
A = P(1 + rt)
\]
Where:
- $A$ = total amount after interest
- $P$ = principal (initial investment) = \$600,000
- $r$ = annual interest rate = 3.5% = 0.035
- $t$ = time (in years) = 6

Now, calculating:
\[
A = 600,000 \times (1 + (0.035 \times 6)) = 600,000 \times (1 + 0.21) = 600,000 \times 1.21 = 726,000
\]

At the end of 6 years, James would earn **\$126,000** in interest with simple interest, and the total amount would be **\$726,000**.

### 2. **Compound Interest Formula**:
The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $A$ = total amount after interest
- $P$ = principal = \$600,000
- $r$ = annual interest rate = 3.5% = 0.035
- $t$ = time = 6 years
- $n$ = number of times the interest is compounded per year (we'll assume yearly, so $n = 1$)

Now, calculating:
\[
A = 600,000 \times \left(1 + \frac{0.035}{1}\right)^{1 \times 6} = 600,000 \times (1.035)^6
\]
Let me compute this value.With compound interest, at the end of 6 years, James would earn approximately **\$137,553.20** in interest, making the total amount **\$737,553.20**.

### Summary:
- **Simple interest**: \$726,000 total (earning \$126,000 in interest).
- **Compound interest**: \$737,553.20 total (earning \$137,553.20 in interest).

Would you like further details or have any questions?

### Related questions:
1. How does the interest calculation change with monthly compounding?
2. What if James invests for 10 years at the same interest rate?
3. How much does the interest amount differ for a 5% interest rate?
4. What is the formula for continuous compounding, and how would it apply here?
5. Can you explain how inflation might affect the real value of James' earnings?

### Tip:
When investing, understanding the difference between simple and compound interest can significantly impact your long-term returns.

James invests $600,000 for 6 years at 3.5% interest rate. How much money would he earn at the end of the period?

Learn how to calculate the amount James would earn from a $600,000 investment over 6 years at a 3.5% interest rate. Explore both simple and compound interest calculations, with detailed formulas and explanations. Suitable for high school students in Grades 9-12.

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