QUESTION 3 SA Credit Bank Mia Parker P. O. Box 472 Kensington Maitland 7405 Dear Ms Parker We know it is important to you to manage your finances responsibly. Here's an offer you would want to use. R9 000,00 Cash already approved YOUR LOAN OFFER AMOUNT ALREADY APPROVED R 9000,00 - Payable over 48 months - Monthly installments R 318,92 EXPIRY DATE: 16 January Calculate the TOTAL amount that Mia has to pay back if she takes the loan. Why, do you think, do banks and other financial institutions offer cash loans to people that did not apply for it? (2) 2 Which investment is the most profitable? Show al calculations. (i) R560 invested at $$ 8 \% $$ $$ \begin{array}{l} \text { R560 invple interest for } \ \text { p.a. simple } \ 3 \text { years } \end{array} $$ $$ 3 \text { years } $$ OR (ii) $$ \begin{array}{l} \text { R } 560 \text { invested at } 7 \% \ \text { p.a. compound } \ \text { interest for } 3 \text { years } \end{array} $$

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1. **Total Amount to Pay Back**

Mia’s loan offer is for $$ R9000.00 $$ to be repaid over 48 months with monthly installments of $$ R318.92 $$. To calculate the total amount payable, multiply the monthly installment by the number of months:

$$
   \text{Total Amount} = 318.92 \times 48
   $$

First, compute the product:

$$
   318.92 \times 48 = 15308.16
   $$

Thus, the total amount Mia has to pay back is:

$$
   R15308.16
   $$

2. **Reason for Pre-Approved Cash Loans**

Banks and financial institutions often offer cash loans to people who did not apply for them in order to:
   
   - Attract new customers and increase their customer base.
   - Generate interest income by encouraging people to borrow money.
   - Utilize pre-qualification processes that identify customers who are likely to meet repayment criteria.
   - Maintain competitiveness in the market by actively marketing attractive financial products.

3. **Comparing Two Investment Options**

We are given two investment options on a principal of $$ R560 $$ over 3 years:

**Option (i): Simple Interest at $$8\%$$ p.a.**

The formula for simple interest is:

$$
   I = P \times r \times t
   $$

Where:
   - $$ P = R560 $$
   - $$ r = 0.08 $$ (8% per annum)
   - $$ t = 3 $$ years

Calculate the interest earned:

$$
   I = 560 \times 0.08 \times 3 = 560 \times 0.24 = 134.40
   $$

The total amount after 3 years is:

$$
   A_{\text{simple}} = P + I = 560 + 134.40 = 694.40
   $$

**Option (ii): Compound Interest at $$7\%$$ p.a.**

Assuming the compound interest is compounded annually, the formula for compound interest is:

$$
   A = P(1 + r)^t
   $$

Where:
   - $$ P = R560 $$
   - $$ r = 0.07 $$ (7% per annum)
   - $$ t = 3 $$ years

Calculate the total amount:

$$
   A_{\text{compound}} = 560(1 + 0.07)^3 = 560(1.07)^3
   $$

First, compute $$ (1.07)^3 $$:

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

Then, calculate $$ A_{\text{compound}} $$:

$$
   A_{\text{compound}} \approx 560 \times 1.225043 \approx 686.02
   $$

(Note: Minor differences in rounding may occur; here we approximate to two decimal places.)

4. **Determining the Most Profitable Investment**

- **Option (i):** Total amount after 3 years is $$ R694.40 $$
   - **Option (ii):** Total amount after 3 years is approximately $$ R686.02 $$

Since $$ R694.40 > R686.02 $$, the investment with simple interest at $$8\%$$ per annum is more profitable.

1. **Total Amount to Pay Back** Mia has to pay back a total of $$ R15,308.16 $$. 2. **Reason for Pre-Approved Cash Loans** Banks offer pre-approved loans to attract new customers, generate interest income, utilize pre-qualification to identify good borrowers, and stay competitive in the market. 3. **Most Profitable Investment** Investing $$ R560 $$ at $$8\%$$ simple interest for 3 years yields $$ R694.40 $$, which is more profitable than investing at $$7\%$$ compound interest, which yields approximately $$ R686.02 $$.

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