To determine the value of your investments after two years, let's break it down step by step:
1. Savings Account
You have saved $6,300.00. You place 30% of this in a savings account.
- Amount in the savings account: \[ \text{Amount in savings} = 0.30 \times 6300 = 1890.00 \]
The savings account earns 3.6% APR compounded annually. The formula for compound interest is: \[ A = P(1 + r)^t \] where:
- \( P \) is the principal amount (initial investment)
- \( r \) is the annual interest rate (decimal)
- \( t \) is the number of years the money is invested or borrowed
For the savings account:
- \( P = 1890.00 \)
- \( r = 0.036 \)
- \( t = 2 \) years
Calculating the amount in the savings account after 2 years: \[ A = 1890(1 + 0.036)^2 \] \[ A = 1890(1.036)^2 \] \[ A \approx 1890(1.072896) \approx 2021.77 \]
2. Stock Plan
The remaining amount from your initial savings is placed in a stock plan.
- Amount in the stock plan: \[ \text{Amount in stock} = 6300 - 1890 = 4410.00 \]
The stock plan decreases by 2.5% in the first year and increases by 8.9% in the second year.
After the first year: \[ \text{Stock value after 1 year} = 4410(1 - 0.025) = 4410 \times 0.975 = 4307.75 \]
After the second year: \[ \text{Stock value after 2 years} = 4307.75(1 + 0.089) = 4307.75 \times 1.089 = 4681.51 \]
3. Total Value After Two Years
Now, we add the final amounts from both the savings account and the stock plan:
\[ \text{Total Value} = \text{Savings Account} + \text{Stock Plan} \] \[ \text{Total Value} = 2021.77 + 4681.51 = 6703.28 \]
Conclusion
After two years, the total value of your investments will be approximately $6,703.28.