The total income of Mr. Teng in the years 2003, 2004 and 2005 was $36,400. His income increased by 20% each year. What was his income in 2005?

Options

A. 5600
B. 8800
C. 10000
D. 14400

Answer

To find Mr. Teng's income in 2005 given that his total income over the years 2003, 2004, and 2005 was $36,400 and that his income increased by 20% each year, we can follow these steps:

### Step 1: Define the income in 2003
Let Mr. Teng's income in 2003 be \( X \).

### Step 2: Calculate the income for 2004
Since his income increases by 20% each year, his income in 2004 can be calculated as:
\[ \text{Income in 2004} = X + 0.20X = X(1 + 0.20) = 1.2X \]

### Step 3: Calculate the income for 2005
Similarly, his income in 2005 will be:
\[ \text{Income in 2005} = 1.2X + 0.20(1.2X) = 1.2X(1 + 0.20) = 1.2X \times 1.2 = 1.44X \]

### Step 4: Set up the equation for total income
The total income over the three years is given by:
\[ \text{Total Income} = X + 1.2X + 1.44X \]
Combining these, we get:
\[ \text{Total Income} = X + 1.2X + 1.44X = (1 + 1.2 + 1.44)X = 3.64X \]

### Step 5: Equate to the total income
According to the problem, the total income over these three years is $36,400. Therefore, we can set up the equation:
\[ 3.64X = 36,400 \]

### Step 6: Solve for \( X \)
To find \( X \), divide both sides by 3.64:
\[ X = \frac{36,400}{3.64} \approx 10,000 \]

### Step 7: Calculate the income for 2005
Now that we have \( X \), we can find the income for 2005:
\[ \text{Income in 2005} = 1.44X = 1.44 \times 10,000 = 14,400 \]

### Conclusion
Thus, Mr. Teng's income in 2005 was **$14,400**.

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