Certainly! Let's break down the solution step by step.
### Problem Understanding:
Jeandri invests R50,000 at an annual interest rate of 9%, compounded yearly. We need to determine how much money she will have after 6 years.
### Solution Steps:
1. Identify the Given Values:
- Initial Investment ([tex]\(P\)[/tex]) = R50,000
- Annual Interest Rate ([tex]\(r\)[/tex]) = 9% = 0.09
- Time Period ([tex]\(t\)[/tex]) = 6 years
2. Understand the Formula for Compound Interest:
The formula to calculate the amount of money ([tex]\(A\)[/tex]) accumulated over time with compound interest is:
[tex]\[
A = P(1 + r/n)^{nt}
\][/tex]
Where:
- [tex]\(P\)[/tex] is the principal amount ([tex]\(P = 50,000\)[/tex])
- [tex]\(r\)[/tex] is the annual interest rate (as a decimal, so 9% becomes 0.09)
- [tex]\(n\)[/tex] is the number of times interest is compounded per year. Since the interest is effective annually, [tex]\(n = 1\)[/tex].
- [tex]\(t\)[/tex] is the number of years the money is invested or borrowed for ([tex]\(t = 6\)[/tex])
3. Apply the Values to the Formula:
Given that [tex]\(n = 1\)[/tex] (interest compounded annually), the formula simplifies to:
[tex]\[
A = P(1 + r)^t
\][/tex]
Substituting the given values, we get:
[tex]\[
A = 50,000(1 + 0.09)^6
\][/tex]
4. Compute the Value:
[tex]\[
A \approx 50,000(1.09)^6
\][/tex]
Using the value provided, we find:
[tex]\[
A \approx 83,855.01
\][/tex]
### Final Answer:
Jeandri will have approximately R83,855.01 after 6 years, given her initial investment of R50,000 at an annual interest rate of 9% compounded yearly.
