1. **Problem Statement:** Sofia plans to save 1200 at the end of each year for 5 years in a bank account with 6% annual interest. We need to find the future value of this ordinary annuity at the end of Year 5.
2. **Formula for Future Value of an Ordinary Annuity:**
$$FV = P \times \frac{(1 + r)^n - 1}{r}$$
where:
- $P$ is the payment each period (1200),
- $r$ is the interest rate per period (0.06),
- $n$ is the number of periods (5).
3. **Substitute the values:**
$$FV = 1200 \times \frac{(1 + 0.06)^5 - 1}{0.06}$$
4. **Calculate $(1 + 0.06)^5$:**
$$1.06^5 = 1.3382255776$$
5. **Calculate numerator:**
$$1.3382255776 - 1 = 0.3382255776$$
6. **Divide by $r$:**
$$\frac{0.3382255776}{0.06} = 5.63709296$$
7. **Multiply by $P$:**
$$1200 \times 5.63709296 = 6764.511552$$
8. **Final answer:**
The future value of the ordinary annuity at the end of Year 5 is approximately **6764.51**.
Future Value Annuity E586E4
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