e) $$ P=A\left(1+\frac{r n}{100}\right) $$ kan gebruik word om die waarde van ' $$ n $$ belegging, $$ P $$, te bereken indien 'n oorspronklike belegging, $$ A $$, teen $$ r \% $$ enkelvoudige rente belê word vir $$ n $$ jare. (1) Maak $$ r $$ die onderwerp van die formule. (2) Bereken $$ r $$ indien $$ A=\mathrm{R} 1000, P=\mathrm{R} 3000 $$ en $$ n=5 $$ jare. LINEERE ONGELYKHEDE

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UpStudy AI · Accepted Answer

Let's solve the problem step by step.

### Step 1: Make $$ r $$ the subject of the formula

The original formula is:

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

To isolate $$ r $$, we can follow these steps:

1. Divide both sides by $$ A $$:

$$
\frac{P}{A} = 1 + \frac{r n}{100}
$$

2. Subtract 1 from both sides:

$$
\frac{P}{A} - 1 = \frac{r n}{100}
$$

3. Multiply both sides by 100:

$$
100\left(\frac{P}{A} - 1\right) = r n
$$

4. Finally, divide both sides by $$ n $$:

$$
r = \frac{100\left(\frac{P}{A} - 1\right)}{n}
$$

Now we have expressed $$ r $$ in terms of $$ P $$, $$ A $$, and $$ n $$.

### Step 2: Calculate $$ r $$ given $$ A = 1000 $$, $$ P = 3000 $$, and $$ n = 5 $$

Now we can substitute the values into the formula we derived:

$$
r = \frac{100\left(\frac{3000}{1000} - 1\right)}{5}
$$

Let's calculate this step by step:

1. Calculate $$ \frac{3000}{1000} $$:

$$
\frac{3000}{1000} = 3
$$

2. Subtract 1:

$$
3 - 1 = 2
$$

3. Multiply by 100:

$$
100 \times 2 = 200
$$

4. Finally, divide by $$ n = 5 $$:

$$
r = \frac{200}{5} = 40
$$

Thus, the value of $$ r $$ is $$ 40\% $$.

### Summary of Results
1. The formula for $$ r $$ is:

$$
r = \frac{100\left(\frac{P}{A} - 1\right)}{n}
$$

2. The calculated value of $$ r $$ is $$ 40\% $$.
$$ r = 40\% $$

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