1. **Problem statement:** A woman deposits 650 at the beginning of each quarter for 5 years into an account paying 8% interest compounded quarterly. We need to find the value of the account at the end of 5 years. 2. **Formula used:** Since deposits are made at the beginning of each period, this is an annuity due. The future value of an annuity due is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$ where: - $P$ = payment per period = 650 - $r$ = interest rate per period = $\frac{8\%}{4} = 0.02$ - $n$ = total number of periods = $5 \times 4 = 20$ 3. **Calculate each component:** - Calculate $(1 + r)^n = (1.02)^{20}$ - Calculate numerator: $(1.02)^{20} - 1$ - Divide by $r = 0.02$ - Multiply by $P = 650$ - Multiply by $(1 + r) = 1.02$ 4. **Intermediate calculations:** - $(1.02)^{20} \approx 1.485947$ - Numerator: $1.485947 - 1 = 0.485947$ - Divide by $0.02$: $\frac{0.485947}{0.02} = 24.29735$ - Multiply by $650$: $24.29735 \times 650 = 15,793.28$ - Multiply by $1.02$: $15,793.28 \times 1.02 = 16,109.15$ 5. **Final answer:** The value of the account at the end of 5 years is approximately **16,109.15**.