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Let's break down the two parts of this problem:

### (a) Find the accumulated amount of RM5000 invested at 6% p.a. compounded semi-annually from 16 April 2000 to 16 April 2002, after which the rate changes to 8% p.a. compounded quarterly until 16 October 2003.

#### Step-by-step breakdown for (a):

1. **Initial Period (16 April 2000 – 16 April 2002):**
   - Principal = RM5000
   - Interest rate = 6% p.a. compounded semi-annually
   - Duration = 2 years

   The formula for compound interest is:
   \[
   A = P \left(1 + \frac{r}{n}\right)^{nt}
   \]
   where:
   - \( P \) = principal amount
   - \( r \) = annual interest rate (decimal)
   - \( n \) = number of times the interest is compounded per year
   - \( t \) = time in years
   - \( A \) = amount accumulated

   For this period:
   - \( P = 5000 \)
   - \( r = 6\% = 0.06 \)
   - \( n = 2 \) (compounded semi-annually)
   - \( t = 2 \) years

   After 2 years, the amount will be:
   \[
   A_1 = 5000 \left(1 + \frac{0.06}{2}\right)^{2 \times 2}
   \]

2. **Second Period (16 April 2002 – 16 October 2003):**
   - Principal = \( A_1 \) (the amount calculated from the first period)
   - Interest rate = 8% p.a. compounded quarterly
   - Duration = 1 year 6 months (1.5 years)

   For this period:
   - \( P = A_1 \)
   - \( r = 8\% = 0.08 \)
   - \( n = 4 \) (compounded quarterly)
   - \( t = 1.5 \) years

   The accumulated amount after 1.5 years will be:
   \[
   A_2 = A_1 \left(1 + \frac{0.08}{4}\right)^{4 \times 1.5}
   \]

Now, let's compute these values.

---

### (b) Find the maturity value of RM8000 invested for 5 years 9 months with two different interest rates:

#### Step-by-step breakdown for (b):

1. **First Period (3 years):**
   - Principal = RM8000
   - Interest rate = 7% p.a. compounded semi-annually
   - Duration = 3 years

   Using the compound interest formula for this period:
   \[
   A_1 = 8000 \left(1 + \frac{0.07}{2}\right)^{2 \times 3}
   \]

2. **Second Period (2 years 9 months = 2.75 years):**
   - Principal = \( A_1 \) (the amount accumulated from the first period)
   - Interest rate = 8% p.a. compounded monthly
   - Duration = 2.75 years

   For this period:
   \[
   A_2 = A_1 \left(1 + \frac{0.08}{12}\right)^{12 \times 2.75}
   \]

Let's calculate both parts (a) and (b). I'll begin by computing the first one.For part (a), the accumulated amount after investing RM5000 at 6% p.a. compounded semi-annually from 16 April 2000 to 16 April 2002, and then at 8% p.a. compounded quarterly until 16 October 2003, is approximately **RM6337.53**.

Now, let's calculate the maturity value for part (b).For part (b), the maturity value after investing RM8000 for 5 years 9 months, with the first 3 years at 7% p.a. compounded semi-annually and the remaining 2 years 9 months at 8% p.a. compounded monthly, is approximately **RM12,245.03**.

Do you want further clarification or a detailed breakdown of any part of these calculations?

Here are 5 related questions you could explore next:
1. How does changing the compounding frequency affect the final investment value?
2. What is the formula for continuous compounding, and how does it differ from discrete compounding?
3. How would the results change if the rates were compounded annually instead?
4. Can you explain how to calculate the effective annual rate (EAR) for different compounding frequencies?
5. What would be the accumulated value if no interest rate change occurred in part (a)?

**Tip:** The more frequent the compounding, the higher the accumulated amount, given the same interest rate and time duration.

On 16 April 2000, RM5000 was invested at 6% p.a. compounded semi-annually. Find the amount accumulated on 16 October 2003 if the rate was changed to 8% p.a. compounded quarterly beginning 16 April 2002.
RM8000 will be invested for 5 years 9 months. If the investment will yield 7% p.a. compounded semi-annually for the 1st 3 years and 8% p.a. compounded monthly for the rest of the period, find the maturity value at the end of the investment period.

This problem involves calculating the accumulated value of RM5000 invested with a changing interest rate, from 6% compounded semi-annually to 8% compounded quarterly. Additionally, RM8000 is invested with different compounding frequencies, requiring a step-by-step solution using compound interest formulas.

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