Part (a): Chen's Investment Growth

Chen invests 40,000 yuan in a fixed-term bond, which pays compound interest at 3.5% per year for 3 years.

The compound interest formula is:

$A = P \times \left(1 + \frac{r}{100}\right)^t$

Where:

• $A$ is the amount after $t$ years,
• $P$ is the initial investment (40,000 yuan),
• $r$ is the interest rate (3.5%),
• $t$ is the number of years (3 years).

Substitute the values into the formula:

$A = 40,000 \times \left(1 + \frac{3.5}{100}\right)^3$ $A = 40,000 \times \left(1.035\right)^3$

Now let's calculate the value of Chen’s investment.

$A = 40,000 \times 1.1087 = 44,347.60$

Rounding to the nearest yuan:

$A \approx 44,348 \, \text{yuan}$

Part (b): Wang's Initial Investment

Wang's investment decreases by 6.5% each year, and after the first year, the value of his investment is 30,481 yuan. To find the initial amount $P$, we use the following formula for depreciation:

$V = P \times \left(1 - \frac{r}{100}\right)$

Where:

• $V = 30,481 \, \text{yuan}$ is the value after the first year,
• $r = 6.5\%$ is the rate of decrease,
• $P$ is the initial value we need to find.

Substitute the values into the formula:

[ 30,481