1. **State the problem:** The Calvarusos invested 40000 in a deferred annuity that will pay monthly for 4 years starting after 14 years. The account earns 2.50% annual interest compounded monthly. We need to find the size of the monthly payments. 2. **Identify the formula:** For a deferred annuity, the present value (PV) of the annuity at time 0 is given by: $$PV = \frac{P \left(1 - (1 + i)^{-n}\right)}{i} \times (1 + i)^{-d}$$ where: - $P$ = monthly payment - $i$ = monthly interest rate - $n$ = total number of payments - $d$ = number of months deferred 3. **Given values:** - $PV = 40000$ - Annual interest rate = 2.50% = 0.025 - Monthly interest rate $i = \frac{0.025}{12} = 0.0020833333$ - Number of payments $n = 4 \times 12 = 48$ - Deferred months $d = 14 \times 12 = 168$ 4. **Rearrange formula to solve for $P$:** $$40000 = \frac{P \left(1 - (1 + 0.0020833333)^{-48}\right)}{0.0020833333} \times (1 + 0.0020833333)^{-168}$$ 5. **Calculate $(1 + i)^{-n}$:** $$ (1 + 0.0020833333)^{-48} = \frac{1}{(1.0020833333)^{48}} \approx \frac{1}{1.104941} = 0.9055$$ 6. **Calculate numerator inside parentheses:** $$1 - 0.9055 = 0.0945$$ 7. **Calculate annuity factor:** $$\frac{0.0945}{0.0020833333} = 45.36$$ 8. **Calculate $(1 + i)^{-d}$:** $$ (1.0020833333)^{-168} = \frac{1}{(1.0020833333)^{168}} \approx \frac{1}{1.3956} = 0.7167$$ 9. **Substitute back:** $$40000 = P \times 45.36 \times 0.7167 = P \times 32.52$$ 10. **Solve for $P$:** $$P = \frac{40000}{32.52} \approx 1230.56$$ **Final answer:** The monthly payment size is approximately **1230.56**.