What amount can be paid into a savings account at the beginning of every 6-month period, instead of R1180 at the end of each month, if interest is calculated at a rate of 2.138% per month? 

To determine the equivalent payment at the beginning of every 6-month period instead of R1180 at the end of each month, we need to account for the change in payment timing and adjust for the compounding interest.

Let's break down the problem into steps:

### Step 1: Define the key variables
- **Monthly payment (PMT)**: R1180
- **Interest rate per month (i)**: 2.138% = 0.02138
- **Compounding period**: Monthly
- **Period of interest**: 6 months

We are looking for the equivalent amount to be paid at the beginning of each 6-month period (denoted as \( P \)).

### Step 2: Calculate the future value (FV) of the monthly payments
The future value of a series of monthly payments at the end of each month can be found using the formula for the future value of an annuity:

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

Where:
- \( PMT \) is the monthly payment (R1180)
- \( i \) is the interest rate per month (0.02138)
- \( n \) is the number of months (6 months for each 6-month period)

### Step 3: Find the equivalent payment at the beginning of each 6-month period
The future value \( FV \) of the monthly payments is equivalent to the payment \( P \) at the beginning of the 6-month period, compounded for 6 months. We can express this as:

\[
FV = P \times (1 + i)^6
\]

### Step 4: Solve for \( P \)
Now, we solve for \( P \) by equating the two expressions for \( FV \).

Let me compute this for you.The equivalent amount to be paid at the beginning of each 6-month period, instead of R1180 at the end of each month, is approximately **R6579.02**.

Would you like more details on how this was calculated, or do you have any further questions?

Here are 5 related questions to explore:
1. How does changing the interest rate affect the payment amount?
2. What happens if the compounding frequency is yearly instead of monthly?
3. How would the result change if payments were made quarterly instead of semi-annually?
4. How can we compute the present value of a future annuity given different interest rates?
5. What if the interest rate were variable instead of fixed?

**Tip:** Always ensure to adjust payment timing when switching between different compounding periods, as this affects the accumulated interest.

What amount can be paid into a savings account at the beginning of every 6-month period, instead of R1180 at the end of each month, if interest is calculated at a rate of 2.138% per month?

Learn how to calculate the equivalent lump sum payment at the beginning of a 6-month period instead of paying R1180 monthly, with a 2.138% monthly interest rate. This example uses key financial mathematics concepts such as the future value of annuities and interest compounding.

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