1. The problem is to calculate the future value (FV) of an investment using the formula for the future value of an annuity: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of periods. 2. Given values: - Monthly interest rate $r = \frac{0.0562}{12}$ - Total periods $n = 12 \times 40 = 480$ - Payment per period $P = 150$ (negative sign indicates cash outflow) 3. Substitute the values into the formula: $$FV = -150 \times \frac{(1 + \frac{0.0562}{12})^{480} - 1}{\frac{0.0562}{12}}$$ 4. Calculate the monthly interest rate: $$r = \frac{0.0562}{12} = 0.0046833$$ 5. Calculate the compound factor: $$ (1 + r)^n = (1 + 0.0046833)^{480}$$ 6. Using a calculator: $$ (1.0046833)^{480} \approx 8.977$$ 7. Calculate the numerator: $$8.977 - 1 = 7.977$$ 8. Calculate the fraction: $$\frac{7.977}{0.0046833} \approx 1703.03$$ 9. Calculate the future value: $$FV = -150 \times 1703.03 = -255454.5$$ 10. The negative sign indicates payments made, so the future value accumulated is approximately 255454.5. 11. The value you mentioned, 269654.74, is close but slightly different due to rounding or calculation method. 12. The difference between 269654.74 and 255454.5 is about 14100, which could be due to rounding or different compounding assumptions. 13. The other numbers 72000 and 197654.74 seem unrelated to this calculation. 14. Therefore, the correct future value using the given formula and inputs is approximately 255454.5. Final answer: $$FV \approx 255454.5$$