3.2. Amukelani want to invest R560 for three years. The bank offers two options Option $$ 1: 8 \% $$ p.a simple interest Option $$ 2: 7 \% $$ p.a compound interest Which investment is the most profitable?

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**Step 1: Calculate Amount with Simple Interest (Option 1)**

Simple interest formula:  
$$
A = P(1 + rt)
$$
where:  
$$ P = 560 $$ (principal),  
$$ r = 0.08 $$ (interest rate per annum),  
$$ t = 3 $$ (time in years).

Substitute the values:
$$
A = 560(1 + 0.08 \times 3) = 560(1 + 0.24) = 560(1.24)
$$

Calculate:
$$
A = 560 \times 1.24 = 694.4
$$

Thus, the investment grows to $$ R694.40 $$ after 3 years in Option 1.

---

**Step 2: Calculate Amount with Compound Interest (Option 2)**

Compound interest formula:  
$$
A = P(1 + r)^t
$$
where:  
$$ P = 560 $$,  
$$ r = 0.07 $$,  
$$ t = 3 $$.

Substitute the values:
$$
A = 560(1 + 0.07)^3 = 560(1.07)^3
$$

Calculate $$ (1.07)^3 $$:
$$
(1.07)^3 \approx 1.225043
$$

Now compute:
$$
A = 560 \times 1.225043 \approx 686.02
$$

Thus, the investment grows to approximately $$ R686.02 $$ after 3 years in Option 2.

---

**Step 3: Compare the Two Options**

- Option 1 (Simple Interest): $$ R694.40 $$  
- Option 2 (Compound Interest): $$ R686.02 $$

Since $$ R694.40 > R686.02 $$, **Option 1 is the most profitable investment**.
Option 1, with simple interest at 8% per annum, yields $$ R694.40 $$ after three years, which is more profitable than Option 2's $$ R686.02 $$ with compound interest at 7% per annum.

3.2. Amukelani want to invest R560 for three years. The bank offers two options Option \( 1: 8 \% \) p.a simple interest Option \( 2: 7 \% \) p.a compound interest Which investment is the most profitable?

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