Future Value 688F9D

1. **State the problem:** Calculate the future value (FV) of monthly investments of $1000 over 360 months at an annual interest rate of 8%. 2. **Identify inputs:** - Number of months (periods), $N = 360$ - Annual interest rate, $8\%$ - Monthly interest rate, $i = \frac{8\%}{12} = 0.0066667$ - Present value, $PV = 0$ (assuming starting from zero) - Monthly payment, $PMT = 1000$ 3. **Formula for future value of an ordinary annuity:** $$FV = PMT \times \frac{(1 + i)^N - 1}{i} + PV \times (1 + i)^N$$ Since $PV = 0$, formula simplifies to: $$FV = PMT \times \frac{(1 + i)^N - 1}{i}$$ 4. **Calculate intermediate values:** $$1 + i = 1 + 0.0066667 = 1.0066667$$ $$ (1 + i)^N = 1.0066667^{360}$$ Calculate $1.0066667^{360}$: $$1.0066667^{360} \approx 10.9356$$ 5. **Calculate numerator:** $$10.9356 - 1 = 9.9356$$ 6. **Calculate fraction:** $$\frac{9.9356}{0.0066667} \approx 1490.34$$ 7. **Calculate future value:** $$FV = 1000 \times 1490.34 = 1,490,340$$ **Final answer:** After 360 months of investing $1000 monthly at 8% annual interest, you will have approximately $1,490,340.