Question 1: Analyze the Business Interest 
Imagine that you are graduating in the year 2027 with a K8,000 account balance. You got a Job at
IBSUniversity in 2028 with a salary of K49000, for which you have to contribute between 10-12%
towards superannuation. The living expenses in Port Moresby must be accounted for. During the 
first year, it was K25,000. In subsequent years, expenses are assumed to increase by 3% each year. 
The remaining amount after living expenses and superannuation contribution are consider to be for 
your house deposit for buying a new house (K300,000). 
The employee’s salary over the next 6 years is predicted to change as follows: 
• At the end of Year 2, a pay increase of 1.25% 
• At the end of Year 4, a pay increase of 2%.
Instructions to answer:
a) Complete the following table 
Year Salary Superannuation Living expenses House Deposit
2028
2029
2030
2031
2032
2033
b) If you do not reach your savings target at the end of 6 years, determine the rate of interest
required for you to reach your goal if all your savings are invested for 6 more years for the interest 
compounded annually.

To solve this problem, we'll break it down into two parts. First, we'll complete the table by calculating the salary, superannuation, living expenses, and house deposit savings for each year. Then, we'll determine the interest rate required if the savings target isn't reached by the end of the 6-year period.

### Part (a): Completing the Table

Here are the given data and assumptions:
- **Initial Salary (2028):** K49,000
- **Superannuation Contribution:** 10% to 12% of the salary (let's assume 10% for simplicity).
- **Living Expenses (2028):** K25,000 (increases by 3% each year).
- **House Price:** K300,000
- **Pay Increase:** 
  - 1.25% at the end of Year 2 (2029).
  - 2% at the end of Year 4 (2031).

We’ll calculate the salary, superannuation, living expenses, and house deposit for each year as follows:

1. **Year 2028:**
   - **Salary:** K49,000
   - **Superannuation (10%):** 0.1 × K49,000 = K4,900
   - **Living Expenses:** K25,000
   - **House Deposit:** Remaining amount after superannuation and living expenses:  
     \( 49,000 - 4,900 - 25,000 = K19,100 \)

2. **Year 2029:**
   - **Salary:** K49,000 (no pay increase yet)
   - **Superannuation (10%):** 0.1 × K49,000 = K4,900
   - **Living Expenses (increase by 3%):** \( 25,000 \times 1.03 = K25,750 \)
   - **House Deposit:** \( 49,000 - 4,900 - 25,750 = K18,350 \)

3. **Year 2030:**
   - **Salary (1.25% increase):** \( 49,000 \times 1.0125 = K49,612.50 \)
   - **Superannuation (10%):** 0.1 × K49,612.50 = K4,961.25
   - **Living Expenses (increase by 3%):** \( 25,750 \times 1.03 = K26,522.50 \)
   - **House Deposit:** \( 49,612.50 - 4,961.25 - 26,522.50 = K18,128.75 \)

4. **Year 2031:**
   - **Salary:** K49,612.50 (no pay increase this year)
   - **Superannuation (10%):** 0.1 × K49,612.50 = K4,961.25
   - **Living Expenses (increase by 3%):** \( 26,522.50 \times 1.03 = K27,318.18 \)
   - **House Deposit:** \( 49,612.50 - 4,961.25 - 27,318.18 = K17,333.07 \)

5. **Year 2032:**
   - **Salary (2% increase):** \( 49,612.50 \times 1.02 = K50,604.75 \)
   - **Superannuation (10%):** 0.1 × K50,604.75 = K5,060.48
   - **Living Expenses (increase by 3%):** \( 27,318.18 \times 1.03 = K28,137.72 \)
   - **House Deposit:** \( 50,604.75 - 5,060.48 - 28,137.72 = K17,406.55 \)

6. **Year 2033:**
   - **Salary:** K50,604.75 (no pay increase this year)
   - **Superannuation (10%):** 0.1 × K50,604.75 = K5,060.48
   - **Living Expenses (increase by 3%):** \( 28,137.72 \times 1.03 = K28,981.85 \)
   - **House Deposit:** \( 50,604.75 - 5,060.48 - 28,981.85 = K16,562.42 \)

Now, let's summarize this in a table:

| Year | Salary (K) | Superannuation (K) | Living Expenses (K) | House Deposit (K) |
|------|------------|-------------------|---------------------|------------------|
| 2028 | 49,000     | 4,900             | 25,000             | 19,100           |
| 2029 | 49,000     | 4,900             | 25,750             | 18,350           |
| 2030 | 49,612.50  | 4,961.25          | 26,522.50          | 18,128.75        |
| 2031 | 49,612.50  | 4,961.25          | 27,318.18          | 17,333.07        |
| 2032 | 50,604.75  | 5,060.48          | 28,137.72          | 17,406.55        |
| 2033 | 50,604.75  | 5,060.48          | 28,981.85          | 16,562.42        |

### Part (b): Calculating the Required Interest Rate

Let's assume the total house deposit savings accumulated over 6 years is not enough to reach the K300,000 goal. We need to determine the interest rate required to reach the goal if these savings are invested for another 6 years with interest compounded annually.

1. **Total House Deposit Savings After 6 Years:**

\[ \text{Total Savings} = 19,100 + 18,350 + 18,128.75 + 17,333.07 + 17,406.55 + 16,562.42 \approx K106,880.79 \]

2. **Amount Needed:** K300,000
3. **Investment Duration:** 6 years
4. **Formula for Compound Interest:**

\[ A = P \left(1 + r\right)^n \]

Where:
- \( A \) = Future value (K300,000)
- \( P \) = Present value (K106,880.79)
- \( r \) = Annual interest rate
- \( n \) = Number of years (6)

We need to solve for \( r \):

\[ 300,000 = 106,880.79 \left(1 + r\right)^6 \]

Dividing both sides by 106,880.79:

\[ \left(1 + r\right)^6 = \frac{300,000}{106,880.79} \approx 2.806 \]

Taking the sixth root of both sides:

\[ 1 + r = \sqrt[6]{2.806} \approx 1.179 \]

So:

\[ r \approx 0.179 \text{ or } 17.9\% \]

### Conclusion:
The required interest rate for the savings to reach K300,000 in 6 years is approximately **17.9%**.

Would you like more details on this, or do you have any questions?

Here are 5 related questions for practice:
1. How would the calculations change if the superannuation rate was 12% instead of 10%?
2. What if the living expenses increased by 5% instead of 3% each year?
3. How much would you need to save annually if the house cost was K400,000 instead of K300,000?
4. How would an annual bonus impact your savings for the house deposit?
5. What would be the impact if the salary increased by 3% every year instead of 1.25% and 2% at intervals?

**Tip:** When solving compound interest problems, always make sure to correctly identify the present value, future value, and the compounding period.

Learn how to calculate salary growth, superannuation contributions, living expenses, and house deposit savings over 6 years. Includes a detailed financial analysis with compound interest calculations. Suitable for adults planning their financial future.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation