What single amount can be invested on 01/03/2020, instead of R1930 at the beginning of every 3-month period, for exactly 3 years (the first investment is made on 01/03/2020), if interest is earned at a rate of 10.384% per year? (Give your answer rounded to 2 decimal places. If you think the answer is R1012.3456, type in 1012.35)

To solve this problem, we need to determine the present value of a series of investments made quarterly over a 3-year period. The present value represents the single amount that can be invested on 01/03/2020 instead of making regular quarterly investments.

Given:
- Quarterly payment: \( R = R1930 \)
- Annual interest rate: 10.384%
- Quarterly interest rate: \( r = \frac{10.384\%}{4} \)
- Total number of payments: 3 years = 12 quarters

The formula to calculate the present value of an annuity (which is what we're dealing with here) is:

\[
PV = R \times \frac{1 - (1 + r)^{-n}}{r}
\]

Where:
- \( PV \) is the present value.
- \( R \) is the quarterly payment.
- \( r \) is the quarterly interest rate.
- \( n \) is the total number of payments.

Let's calculate the present value using these values.The single amount that can be invested on 01/03/2020 instead of making quarterly payments of R1930 for 3 years is **R19,682.90**.

Would you like further explanation or have any other questions? Here are some related questions you might be interested in:

1. How does the frequency of compounding affect the present value of an investment?
2. What is the future value of the same series of investments after 3 years?
3. How would the present value change if the interest rate were higher?
4. What happens if the payments are made monthly instead of quarterly?
5. Can we calculate the total amount paid if we continue with the quarterly payments?

**Tip:** Understanding the concept of present value is crucial in comparing different investment options or payment plans, especially when interest is involved.

Learn how to calculate the present value of quarterly investments made over 3 years at a 10.384% annual interest rate. Understand the concept of present value in finance and annuities. Detailed solution provided with step-by-step calculation.

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