Answer:
To calculate the future value of a sinking fund where a company invests a fixed amount annually at a given interest rate, we use the Future Value of an Annuity formula. The formula for the future value of an ordinary annuity (where payments are made at the end of each period) is:
\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]
where:
- \( FV \) is the future value of the annuity.
- \( P \) is the annual payment (Shs. 30,000).
- \( r \) is the annual interest rate (9% or 0.09).
- \( n \) is the number of years the payments are made (5 years).
Let's plug the values into the formula and calculate step by step:
1. **Identify the values:**
- \( P = 30,000 \)
- \( r = 0.09 \)
- \( n = 5 \)
2. **Calculate \( (1 + r)^n \):**
\[ (1 + 0.09)^5 = 1.09^5 \]
Using a calculator to compute \( 1.09^5 \):
\[ 1.09^5 \approx 1.53862 \]
3. **Subtract 1 from \( (1 + r)^n \):**
\[ 1.53862 - 1 = 0.53862 \]
4. **Divide by \( r \):**
\[ \frac{0.53862}{0.09} \approx 5.98467 \]
5. **Multiply by the annual payment \( P \):**
\[ FV = 30,000 \times 5.98467 \approx 179,540.10 \]
So, the sinking fund will be worth approximately Shs. 179,540.10 after 5 years.
