1. **Problem Statement:** We want to find the lump sum deposited today that will yield the same total amount as payments of 20000 at the end of each year for 6 years, with an interest rate of 3% compounded annually. 2. **Formula to Use:** This is a problem involving the present value of an ordinary annuity. The formula for the present value $PV$ of an annuity with payment $P$, interest rate $r$, and number of periods $n$ is: $$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$ 3. **Explanation:** - $P$ is the payment amount each period (20000). - $r$ is the interest rate per period (0.03). - $n$ is the number of payments (6). This formula calculates the lump sum amount that, if invested today at the given interest rate, will grow to the same value as the series of payments. 4. **Intermediate Work:** - Substitute the values: $$PV = 20000 \times \frac{1 - (1 + 0.03)^{-6}}{0.03}$$ - Calculate $(1 + 0.03)^{-6} = 1.03^{-6}$. - Then compute the fraction and multiply by 20000. 5. **Interpretation:** The lump sum calculated by this formula is the amount that needs to be deposited today to be equivalent to receiving 20000 at the end of each year for 6 years at 3% interest compounded annually. **Final answer:** The formula to calculate the lump sum is: $$PV = 20000 \times \frac{1 - (1 + 0.03)^{-6}}{0.03}$$