Chen invests 40 000 yuan in a fixed-term bond for 3 years.
The fixed-term bond pays compound interest at a rate of 3.5% each year.
(a) Work out the value of Chen’s investment at the end of 3 years.
Give your answer to the nearest yuan.

...................................................... yuan
(3)

Wang invested P yuan.
The value of his investment decreased by 6.5% each year.
At the end of the first year, the value of Wang’s investment was 30481 yuan.
(b) Work out the value of P.

### 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

Chen invests 40,000 yuan in a fixed-term bond for 3 years. The fixed-term bond pays compound interest at a rate of 3.5% each year. (a) Work out the value of Chen’s investment at the end of 3 years. Give your answer to the nearest yuan. ...................................................... yuan (3) Wang invested P yuan. The value of his investment decreased by 6.5% each year. At the end of the first year, the value of Wang’s investment was 30,481 yuan. (b) Work out the value of P.

Learn how to calculate the future value of investments using compound interest and determine the initial value of a depreciating investment. This problem involves calculating the final amount of a 40,000 yuan investment with 3.5% annual interest over 3 years and finding the initial amount of an investment decreasing by 6.5% each year. Suitable for students in Grades 10-12.

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