Subjects finance

Future Value Annuity E586E4

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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**.