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Let’s work through the questions one by one from the image you've provided. There are three major parts in the question, so I'll guide you through each.

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### Question 6.1:
"The value of a vehicle worth R150,000 depreciates at 13% p.a. Calculate the value of the vehicle in 6 years if depreciation is calculated on the reducing-balance method."

The reducing-balance depreciation formula is:
\[
V = P(1 - r)^t
\]
Where:
- \( V \) is the value of the vehicle after \( t \) years.
- \( P = 150,000 \) is the initial value of the vehicle.
- \( r = 13\% = 0.13 \) is the annual depreciation rate.
- \( t = 6 \) years.

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### Question 6.2:
#### 6.2.1:
"A loan of R300,000 is taken out at an interest rate of 5.5% p.a., compounded quarterly. The loan was taken out on the 1st of March 2016, and the first repayment is made on 1 December 2016. It is repaid in 72 equal quarterly payments."

You are asked to find the outstanding balance of the loan on **1 September 2016**.

To calculate this, we need to use the formula for compound interest:
\[
A = P\left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \( A \) is the amount after interest.
- \( P = 300,000 \) is the principal loan amount.
- \( r = 5.5\% = 0.055 \) is the annual interest rate.
- \( n = 4 \) (compounded quarterly).
- \( t \) will be calculated from **March 1st to September 1st** (half a year).

#### 6.2.2:
"Determine the quarterly repayments required to pay back the loan."

We will use the annuity formula to determine the quarterly repayments:
\[
R = \frac{P \times \frac{r}{n}}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]
Where \( R \) is the quarterly payment, and the other variables are the same as defined above.

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### Question 6.3:
"East landed a job which remunerated him R7,562.50 quarterly. He then decided to open an investment account and deposit 11% of his salary at the end of every quarter into the investment account, earning an interest of 7.5% p.a. compounded monthly for 8 years."

The future value of the investment can be calculated using the formula for the future value of an ordinary annuity:
\[
A = R \times \frac{\left(1 + \frac{i}{n}\right)^{nt} - 1}{\frac{i}{n}}
\]
Where:
- \( R = 7,562.50 \times 0.11 \) is the deposit amount per quarter.
- \( i = 7.5\% = 0.075 \) is the interest rate.
- \( n = 12 \) (compounded monthly).
- \( t = 8 \) years.

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Let me solve each part step by step now.Here are the solutions for each part of the question:

### 6.1 Depreciation Calculation:
The value of the vehicle after 6 years is approximately **R65,043.93**.

### 6.2.1 Outstanding Loan Balance:
The outstanding balance of the loan on **1 September 2016** is approximately **R308,306.72**.

### 6.2.2 Quarterly Repayments:
The required quarterly repayment to pay back the loan in 72 payments (18 years) is approximately **R6,590.42**.

### 6.3 Investment Account Future Value:
The amount in the investment account at the end of 8 years will be approximately **R108,971.59**.

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Would you like more details on any of these calculations or clarifications?

Here are 5 related questions for further practice:
1. How does increasing the depreciation rate affect the vehicle's value after 6 years?
2. If the loan interest rate was 6.5% instead of 5.5%, what would the outstanding balance be?
3. What if the loan repayments were made monthly instead of quarterly?
4. How would the investment account value change if the interest rate was compounded quarterly instead of monthly?
5. How much would the investment account hold if East deposited 15% of his salary instead of 11%?

**Tip:** Always check whether interest is compounded monthly, quarterly, or yearly to use the correct formula.

6.1 The value of a vehicle worth R150,000 depreciates at 13% p.a. Calculate the value of the vehicle in 6 years if depreciation is calculated on the reducing-balance method.
6.2 A loan of R300,000 is taken out at an interest rate of 5.5% p.a. compounded quarterly. The loan was taken out on 1 March 2016, and it is repaid in 72 equal quarterly payments. 6.2.1 What is the outstanding balance of the loan on 1 September 2016? 6.2.2 Determine the quarterly repayments required to pay back the loan.
6.3 East landed a job that remunerated him R7,562.50 quarterly. He then decided to open an investment account and deposit 11% of his salary at the end of every quarter into the investment account, earning interest of 7.5% p.a. compounded monthly for 8 years. What amount will be in the account at the end of eight years?

This problem involves calculating the depreciated value of a vehicle over 6 years, the outstanding balance of a loan after six months, and the future value of an investment using compound interest and annuity formulas. Ideal for students in Grades 11-12.

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