K95 is invested into an account at the end of every 4 months for 2 years and 8 months at 15% p.a. compounded every 4 months.

1. (a) Calculate how much you would have in this account at the end of this period?


2. (b) Calculate the present value?


3. (c) Evaluate the equivalent lump-sum for this investment.

To solve this problem, we will apply the concept of compound interest for part (a), the present value formula for part (b), and the future value equivalent for part (c).

### Given dataTo solve this problem, we will apply the concept of compound interest for part (a), the present value formula for part (b), and the future value equivalent for part (c).

### Given 
- Periodic investment: K95 (every 4 months)
- Duration: 2 years and 8 months (which is equivalent to 32 months, or \( \frac{32}{4} = 8 \) periods of 4 months)
- Interest rate: 15% per annum compounded every 4 months, which gives \( i = \frac{15\%}{3} = 5\% \) per 4-month period

#### 1. (a) **Calculate the total amount at the end of the period**

We are dealing with an **ordinary annuity**, where periodic payments are made at the end of each period, and interest is compounded periodically.

The formula for the future value \( FV \) of an ordinary annuity is:

\[
FV = P \times \left[ \frac{(1 + i)^n - 1}{i} \right]
\]

Where:
- \( P = 95 \) (the periodic payment)
- \( i = 0.05 \) (the interest rate per period)
- \( n = 8 \) (the number of periods)

Let me calculate that.The total amount in the account at the end of the period would be approximately **K907.17**.

---

#### 1. (b) **Calculate the present value**

To calculate the present value (PV) of an ordinary annuity, we use the formula:

\[
PV = P \times \left[ \frac{1 - (1 + i)^{-n}}{i} \right]
\]

Let me calculate this next.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to walk through the steps for calculating the present value manually, or do you have any other questions?

Here are five related questions to deepen your understanding:

1. How would the future value change if the interest rate were 10% per annum instead of 15%?
2. What would happen if the compounding was done monthly instead of every 4 months?
3. How does the number of periods affect both the future and present values?
4. How would the lump-sum equivalent change if the payments were made at the start of each period (annuity due)?
5. What is the difference between present value and future value in the context of an annuity?

**Tip:** When calculating the present value, you are essentially figuring out how much the future cash flows are worth today at a given interest rate.

K95 is invested into an account at the end of every 4 months for 2 years and 8 months at 15% p.a. compounded every 4 months.
1. (a) Calculate how much you would have in this account at the end of this period?
2. (b) Calculate the present value?
3. (c) Evaluate the equivalent lump-sum for this investment.

Explore the detailed solution for calculating the future value, present value, and lump-sum equivalent of periodic investments at a 15% annual interest rate compounded every 4 months. This problem applies compound interest and annuity formulas, suitable for students and professionals in finance and math.

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