Round any decimals to the nearest penny.

Question

You invest $2000 in a stock plan and another $2000 in a savings
account. The stock plan decreases by 7% the first year and gains
10% the second year. The savings account earns 3.7% APR and
compounds annually. What is the difference in earnings between
the stock and savings account at the end of the second year?

Answer 1

Let's calculate the value of the investment in the stock plan and the savings account after two years.

Stock Plan:

1. Initial Investment: $2000
2. Year 1: Decrease by 7% \[ \text{Value after Year 1} = 2000 - (2000 \times 0.07) = 2000 - 140 = 1860 \]
3. Year 2: Increase by 10% \[ \text{Value after Year 2} = 1860 + (1860 \times 0.10) = 1860 + 186 = 2046 \]

Savings Account:

1. Initial Investment: $2000
2. Annual Interest Rate: 3.7% compounded annually
3. Value after Year 1: \[ \text{Value after Year 1} = 2000 + (2000 \times 0.037) = 2000 + 74 = 2074 \]
4. Value after Year 2: \[ \text{Value after Year 2} = 2074 + (2074 \times 0.037) = 2074 + 76.738 = 2150.738 \]

Now rounding to the nearest penny:

• Stock Plan after 2 years: \(2046.00\)
• Savings Account after 2 years: \(2150.74\)

Difference in Earnings:

\[ \text{Difference} = 2150.74 - 2046.00 = 104.74 \]

Thus, the difference in earnings between the stock plan and the savings account at the end of the second year is $104.74.