Question 2 2. Divide R55000 in the rallo $$ 4: 0: 7 $$ 2. A pair of jeane marked at $$ \mathrm{k} 460,00 $$ ls aold at a discount of $$ 20 \% $$. Determine the selling price. (d) (3) 2. With the use of the following formula, determine the fifure value of 'Steven's monoy. Round ALL. thie answer off to 2 decimal places. $$ A=P(1+i n) $$ Steven won a portion of the local lotery, 'Thie price money is to tho value of R18 000 . He wants to invest the monoy but docs not know which bank to choose. FNB offers Stoven $$ 5,6 \% $$ for 8 years simple interest por mumm, Nedbank offers Stoven $$ 6,6 \% $$ for 6 years simple interest per anaum and Standard Bank offers $$ 7,2 \% $$ for 5 years almplo interest. Determine each bank's futuro value to help Steven deeide whith bank ho should choose. FNB Nedbank Standard Bank (9)

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UpStudy AI · Accepted Answer

**Problem 2.1: Division of R55000 in the Ratio $$4:0:7$$**

1. Calculate the total number of parts:
   $$
   4 + 0 + 7 = 11 \text{ parts}
   $$
2. Determine the value of one part:
   $$
   \text{Value per part} = \frac{55000}{11} = 5000
   $$
3. The first share (4 parts):
   $$
   4 \times 5000 = 20000
   $$
4. The second share (0 parts):
   $$
   0 \times 5000 = 0
   $$
5. The third share (7 parts):
   $$
   7 \times 5000 = 35000
   $$

So, the amounts are:
- First: R20000  
- Second: R0  
- Third: R35000

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**Problem 2.2: Selling Price of Jeans**

1. The marked price is $$ R460 $$.
2. The discount given is $$ 20\% $$. Calculate the discount amount:
   $$
   \text{Discount} = 0.20 \times 460 = 92
   $$
3. Subtract the discount from the marked price:
   $$
   \text{Selling price} = 460 - 92 = 368
   $$

Thus, the selling price is R368.

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**Problem 2.3: Future Value of Steven's Lottery Money**

Steven has $$ P = R18000 $$. The formula for simple interest is:
$$
A = P(1+in)
$$
where $$ i $$ is the interest rate (in decimal form) and $$ n $$ is the number of years.

1. **FNB:**
   - Interest rate: $$ 5.6\% = 0.056 $$
   - Time: $$ 8 $$ years
   $$
   A = 18000\left(1 + 0.056 \times 8\right) = 18000\left(1 + 0.448\right) = 18000 \times 1.448 = 26064
   $$
   
2. **Nedbank:**
   - Interest rate: $$ 6.6\% = 0.066 $$
   - Time: $$ 6 $$ years
   $$
   A = 18000\left(1 + 0.066 \times 6\right) = 18000\left(1 + 0.396\right) = 18000 \times 1.396 = 25128
   $$
   
3. **Standard Bank:**
   - Interest rate: $$ 7.2\% = 0.072 $$
   - Time: $$ 5 $$ years
   $$
   A = 18000\left(1 + 0.072 \times 5\right) = 18000\left(1 + 0.36\right) = 18000 \times 1.36 = 24480
   $$

To decide which bank Steven should choose, compare the future values:
- FNB: R26064  
- Nedbank: R25128  
- Standard Bank: R24480

FNB offers the highest future value.

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**Problem 2.1: Division of R55000 in the Ratio $$4:0:7$$** - First share: R20,000 - Second share: R0 - Third share: R35,000 **Problem 2.2: Selling Price of Jeans** - Selling price: R368 **Problem 2.3: Future Value of Steven's Lottery Money** - FNB: R26,064 - Nedbank: R25,128 - Standard Bank: R24,480 Steven should choose FNB for the highest future value.

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