2.) Assuming that you have been given a 500,000/= tax free gift and have decided to invest in a 2
year certificate of deposits which compounds interest semi-annually, how much will you have when
the deposit matures if the interest rate is 14%?

To calculate how much you'll have when the deposit matures after 2 years, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A \) is the amount of money you'll have when the deposit matures.
- \( P \) is the initial principal (500,000).
- \( r \) is the annual interest rate (14% or 0.14).
- \( n \) is the number of times the interest is compounded per year (since it is compounded semi-annually, \( n = 2 \)).
- \( t \) is the time the money is invested or borrowed for, in years (2 years in this case).

Now, let's calculate it.

\[
A = 500,000 \left(1 + \frac{0.14}{2}\right)^{2 \times 2}
\]

\[
A = 500,000 \left(1 + 0.07\right)^{4}
\]

\[
A = 500,000 \left(1.07\right)^{4}
\]

Let's compute this value.The amount you'll have when the deposit matures after 2 years, with semi-annual compounding at a 14% interest rate, is approximately **655,398.01**.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How would the final amount change if the interest compounded quarterly instead?
2. What is the difference between simple and compound interest in this scenario?
3. How would the investment grow if the interest rate was reduced to 10%?
4. What would happen if the investment period was increased to 5 years?
5. How does the frequency of compounding affect the final amount?

**Tip:** The more frequently interest is compounded, the more you'll earn due to the effect of interest on interest.

Assuming that you have been given a 500,000/= tax-free gift and have decided to invest in a 2-year certificate of deposits which compounds interest semi-annually, how much will you have when the deposit matures if the interest rate is 14%?

Learn how to calculate the future value of a 500,000 tax-free gift invested in a 2-year certificate of deposit, with semi-annual compounding at 14% interest. This example covers compound interest and exponential growth concepts, suitable for students in Grades 9-12.

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