1. **State the problem:** Alain Dupre wants to set up a scholarship fund that pays $3,700 annually, starting 5 years after his initial deposit. The fund earns 3.6% interest compounded annually. We need to find how much Alain must deposit now. 2. **Identify the formula:** This is a problem involving the present value of an annuity deferred for 5 years. The formula for the present value of an annuity immediate is: $$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$ where $P$ is the annual payment, $r$ is the annual interest rate, and $n$ is the number of payments. 3. **Adjust for the 5-year delay:** Since payments start 5 years later, the present value at the time of the first payment (year 5) is calculated first, then discounted back 5 years to the present. 4. **Calculate the present value at year 5:** $$P = 3700, \quad r = 0.036, \quad n = \text{number of payments (assumed infinite or not specified, so assume perpetuity)}$$ Since the number of payments is not specified, we assume a perpetuity starting at year 5. 5. **Present value of perpetuity at year 5:** $$PV_{5} = \frac{P}{r} = \frac{3700}{0.036} = 102777.777778$$ 6. **Discount $PV_5$ back to present (year 0):** $$PV_0 = PV_5 \times (1 + r)^{-5} = 102777.777778 \times (1.036)^{-5}$$ Calculate: $$ (1.036)^5 = 1.193052 $$ So, $$PV_0 = 102777.777778 \times \frac{1}{1.193052} = 102777.777778 \times 0.838486 = 86125.68$$ 7. **Final answer:** Alain must deposit approximately **86125.68** now to fund the scholarship payments starting 5 years later.