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Let's go through each part of the problem step by step.

### (a) If $1000 is invested at 5% simple interest (p.a.), find the amount accrued over a period of 5 years.

The formula for simple interest is:

\[
A = P(1 + rt)
\]

Where:
- $ A $ is the accrued amount (total).
- $ P = 1000 $ is the principal.
- $ r = 5\% = 0.05 $ is the annual interest rate.
- $ t = 5 $ years is the time.

Substituting the given values into the formula:

\[
A = 1000(1 + 0.05 \times 5)
\]

Let me calculate the accrued amount.

### (b) Find the simple interest rate when $200 invested accrued to an amount of $260 at the end of year 3.

Using the simple interest formula again:

\[
A = P(1 + rt)
\]

Given:
- $ P = 200 $
- $ A = 260 $
- $ t = 3 $ years

We need to find $ r $. Rearranging the formula to solve for $ r $:

\[
r = \frac{A - P}{P \cdot t}
\]

Substituting the values:

\[
r = \frac{260 - 200}{200 \times 3}
\]

I will compute the value of $ r $ next.

### (c) Find the principal amount that should be invested with 8% simple interest (p.a.) if you wish to get $2800 over a period of 5 years.

We will use the same simple interest formula:

\[
A = P(1 + rt)
\]

Given:
- $ A = 2800 $
- $ r = 8\% = 0.08 $
- $ t = 5 $ years

We need to find $ P $. Rearranging the formula to solve for $ P $:

\[
P = \frac{A}{1 + rt}
\]

Substituting the values:

\[
P = \frac{2800}{1 + 0.08 \times 5}
\]

Let me calculate this for you. I'll now solve all three parts.Here are the solutions to the given problems:

### (a) Amount accrued after 5 years:
\[
A = 1250.00
\]
So, the total amount accrued after 5 years is **$1250.00**.

### (b) Simple interest rate:
The simple interest rate is:
\[
r = 0.10 = 10\%
\]
Thus, the interest rate is **10%** per annum.

### (c) Principal amount to invest:
The principal amount that should be invested is:
\[
P = 2000.00
\]
So, **$2000.00** should be invested to get $2800 over 5 years at 8% interest.

Do you need any further clarifications?

---

Here are 5 related questions:
1. How would the accrued amount change if the interest rate in part (a) was 6%?
2. What is the formula for compound interest, and how does it differ from simple interest?
3. How much more would you have if you invested $2000 at 10% for 7 years instead of 5 years?
4. If the time in part (c) was 10 years instead of 5, how much would need to be invested?
5. What would the total amount be in part (a) if compounded annually instead of simple interest?

**Tip:** To solve for variables in interest-related problems, rearranging the formula as needed is essential to avoid confusion.

If $1000 is invested at 5% simple interest (p.a.), find the amount accrued over a period of 5 years. Find the simple interest rate when $200 invested accrued to $260 at the end of year 3 after investment. Find the principal amount that should be invested with 8% simple interest (p.a.) if you wish to get $2800 over a period of 5 years.

Solve problems involving simple interest calculations including accrued amount, interest rate, and principal investment. This step-by-step guide covers a scenario with $1000 invested at 5%, a $200 investment growing to $260, and calculating the necessary principal to earn $2800 at 8%.

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