Connor invests a sum of money at an interest rate of 3% per year compounded annually. The value of the investment, y, after n years can be calculated using the equation `y=A(x)^(n)`. If Connor invests $250 and wants to calculate the value of his investment after 10 years, assuming no further deposits or withdrawals, which of the following equations should be use?

Options

A. `y=250(0.97)^(10)`
B. `y=(250xx0.03)^(10)`
C. `y=250(0.03)^(10)`
D. `y=250(1.03)^(10)`

Answer

To solve the problem of calculating the future value of Connor's investment after 10 years with an interest rate of 3% compounded annually, we can follow these steps:

### Step 1: Identify the variables in the compound interest formula
The formula for compound interest is given by:
\[ y = P \times (1 + r)^n \]
where:
- \( y \) is the final amount of the investment,
- \( P \) is the principal amount (the initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( n \) is the number of years the money is invested.

### Step 2: Substitute the known values into the formula
In this case:
- \( P = 250 \) (the initial investment),
- \( r = 3\% = \frac{3}{100} = 0.03 \) (the interest rate as a decimal),
- \( n = 10 \) (the number of years).

Now substituting these values into the formula:
\[ y = 250 \times (1 + 0.03)^{10} \]

### Step 3: Simplify the equation
Now, simplify the expression inside the parentheses:
\[ y = 250 \times (1.03)^{10} \]

### Step 4: Calculate \( (1.03)^{10} \)
Using a calculator or exponentiation:
\[ (1.03)^{10} \approx 1.3439 \]
Now substitute this back into the equation:
\[ y \approx 250 \times 1.3439 \]

### Step 5: Calculate the final amount
Now perform the multiplication:
\[ y \approx 250 \times 1.3439 \approx 335.975 \]

### Step 6: Round to the nearest cent
Since we are dealing with currency, we round to two decimal places:
\[ y \approx 335.98 \]

### Final Answer
Thus, the value of Connor's investment after 10 years will be approximately **$335.98**.