1. **State the problem:** Frances wants to have $325,000 in 5 years by making 6 equal deposits: one today and one at the end of each of the next 5 years, into an account with 4.2% annual interest. 2. **Identify the formula:** This is an annuity due problem because deposits are made at the beginning of each period (today and then at the end of each year). The future value of an annuity due is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$ where: - $FV$ is the future value ($325,000$), - $P$ is the payment per period (what we want to find), - $r$ is the interest rate per period ($0.042$), - $n$ is the number of payments ($6$). 3. **Plug in the values:** $$325000 = P \times \frac{(1 + 0.042)^6 - 1}{0.042} \times (1 + 0.042)$$ 4. **Calculate the terms:** Calculate $(1 + 0.042)^6$: $$1.042^6 = 1.042 \times 1.042 \times 1.042 \times 1.042 \times 1.042 \times 1.042 = 1.276281$$ Calculate numerator: $$1.276281 - 1 = 0.276281$$ Calculate fraction: $$\frac{0.276281}{0.042} = 6.57907$$ Multiply by $(1 + 0.042)$: $$6.57907 \times 1.042 = 6.8573$$ 5. **Solve for $P$:** $$325000 = P \times 6.8573$$ Divide both sides by 6.8573: $$P = \frac{325000}{6.8573}$$ Show cancellation: $$P = \frac{325000}{\cancel{6.8573}} \times \frac{\cancel{1}}{1}$$ Calculate: $$P = 47388.68$$ 6. **Final answer:** Each deposit must be **47388.68** to reach $325,000 in 5 years with 6 deposits at 4.2% interest.