1. **Problem Statement:** Suppose you want to save for a vacation and decide to deposit 1000 every year into a savings account that pays 5% annual interest. You plan to make these deposits at the end of each year for 5 years. How much money will you have in the account at the end of 5 years? 2. **Formula Used:** For a deferred annuity where payments start at the end of each period, the future value (FV) is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $P$ is the payment amount per period, - $r$ is the interest rate per period, - $n$ is the number of payments. 3. **Explanation:** - Each payment earns interest for a different number of years depending on when it was deposited. - The formula sums the future values of all payments. 4. **Calculation:** Given $P = 1000$, $r = 0.05$, and $n = 5$: $$FV = 1000 \times \frac{(1 + 0.05)^5 - 1}{0.05}$$ Calculate the numerator: $$(1.05)^5 = 1.2762815625$$ So: $$FV = 1000 \times \frac{1.2762815625 - 1}{0.05} = 1000 \times \frac{0.2762815625}{0.05}$$ Simplify: $$FV = 1000 \times 5.52563125 = 5525.63$$ 5. **Answer:** At the end of 5 years, you will have approximately $5525.63 in the account.