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Let's go through each part of the question:

### Question 6.1
The value of a vehicle worth R150,000 depreciates at 13% per annum. You are asked to calculate the value of the vehicle after 6 years, assuming depreciation is calculated using the reducing balance method.

The formula for depreciation under the reducing balance method is:
\[
V = P(1 - r)^t
\]
Where:
- \(V\) = value after depreciation
- \(P\) = initial value (R150,000)
- \(r\) = depreciation rate (13% = 0.13)
- \(t\) = time in years (6 years)

Substituting into the formula, we get:
\[
V = 150000(1 - 0.13)^6
\]

### Question 6.2.1
A loan of R300,000 is taken at 5.5% per annum, compounded quarterly. The loan was taken out on 1st March 2016, and the first payment is made on 1st December 2016. The question asks for the outstanding balance on 1st September 2016.

For loans compounded quarterly, the formula is:
\[
A = P(1 + \frac{r}{n})^{nt}
\]
Where:
- \(A\) = amount after compounding
- \(P\) = principal (R300,000)
- \(r\) = annual interest rate (5.5% = 0.055)
- \(n\) = number of times compounded per year (4 for quarterly)
- \(t\) = time in years (from March to September is 6 months or 0.5 years)

So we calculate the outstanding balance.

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

The formula for calculating repayments for a loan compounded periodically is:
\[
R = \frac{P \cdot \frac{r}{n}}{1 - (1 + \frac{r}{n})^{-nt}}
\]
Where \(R\) is the periodic repayment amount, and the other variables are as defined above.

### Question 6.3
A person receives R7,562.50 quarterly and decides to invest 11% of this into an account earning 7.8% interest per annum, compounded quarterly. We need to calculate the amount in the account after 8 years.

The formula for future value of regular investments is:
\[
FV = P \times \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}}
\]
Where:
- \(FV\) = future value of the investment
- \(P\) = quarterly investment (11% of R7,562.50)
- \(r\) = annual interest rate (7.8% = 0.078)
- \(n\) = number of times compounded per year (4 for quarterly)
- \(t\) = time in years (8 years)

Let me calculate these values for you.Here are the calculations for each part of the question:

### 6.1 Depreciation of the vehicle:
The value of the vehicle after 6 years, using the reducing balance method, will be approximately **R65,043.93**.

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

### 6.2.2 Quarterly repayments to pay off the loan:
The quarterly repayments required to pay back the loan over 72 payments is approximately **R6,590.42**.

### 6.3 Investment amount after 8 years:
The amount in the investment account at the end of 8 years will be approximately **R36,483.17**.

Would you like any further details or have any questions? Here are some related questions you might find helpful:

1. How does the reducing balance method differ from straight-line depreciation?
2. What factors affect the repayment amount for a loan?
3. How do different compounding periods (monthly, quarterly) affect loan balances?
4. How can investment returns be maximized in compound interest scenarios?
5. How does inflation affect the real value of investments over time?

**Tip:** When planning long-term investments, consider both the interest rate and the compounding frequency, as more frequent compounding increases the total return.

The value of a vehicle worth R150,000 depreciates at 13% per annum. Calculate the value of the vehicle in 6 years if depreciation is calculated using the reducing balance method. A loan of R300,000 is taken out at an interest rate of 5.5% per annum, compounded quarterly. The loan was taken on the 1st of March 2016, and the first payment was made on 1st December 2016. Determine the outstanding balance of the loan on 1st September 2016, and calculate the quarterly repayments required. A person receives R7,562.50 quarterly and deposits 11% in an account earning 7.8% interest, compounded quarterly, for 8 years. Calculate the final balance.

Learn how to solve depreciation, loan repayment, and future investment problems. The problem includes calculating the value of a vehicle using the reducing balance method, determining the outstanding loan balance with compound interest, and estimating future investment value after 8 years with regular deposits.

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