Question

You save $5000 and invest 60% of it in stocks while leaving the rest
in a savings account earning 4.9% APR. The stock increases 9% in the
first year and loses 4% of its value the second year. What is the total
gained during the 2 years?

Answer 1

Let's break this down step by step.

1. **Initial Investment Breakdown:**
- Total savings: $5000
- Investment in stocks: 60% of $5000
\[
\text{Investment in stocks} = 0.6 \times 5000 = 3000
\]
- Amount in savings account: 40% of $5000
\[
\text{Amount in savings} = 0.4 \times 5000 = 2000
\]

2. **Stock Investment Performance:**
- In the first year, the stock increases by 9%.
\[
\text{Value after Year 1} = 3000 \times (1 + 0.09) = 3000 \times 1.09 = 3270
\]
- In the second year, the stock loses 4%.
\[
\text{Value after Year 2} = 3270 \times (1 - 0.04) = 3270 \times 0.96 = 3139.20
\]

3. **Savings Account Interest:**
- The savings account earns 4.9% APR for 2 years. The formula for the amount in the savings account after 2 years is:
\[
\text{Future Value} = \text{Principal} \times (1 + r)^n
\]
- Where \( r = 0.049 \) (4.9%) and \( n = 2 \):
\[
\text{Future Value} = 2000 \times (1 + 0.049)^2 = 2000 \times (1.049)^2 \approx 2000 \times 1.100801 = 2201.60
\]

4. **Total Amount After 2 Years:**
- Adding the value of stocks and the savings account:
\[
\text{Total Amount} = \text{Value of Stocks} + \text{Future Value of Savings} = 3139.20 + 2201.60 = 5340.80
\]

5. **Total Gain:**
- The total gain is the total amount after 2 years minus the initial investment:
\[
\text{Total Gain} = \text{Total Amount} - \text{Initial Investment} = 5340.80 - 5000 = 340.80
\]

Thus, the total gained during the 2 years is **$340.80**.