1. **State the problem:** Calculate the payment (PMT) that will produce a future value (A) of 36000 with an interest rate of 8% compounded monthly over 70 periods. 2. **Formula used:** The future value of an annuity formula is $$A = PMT \times \frac{(1 + r)^n - 1}{r}$$ where $A$ is the future value, $PMT$ is the payment per period, $r$ is the interest rate per period, and $n$ is the number of periods. 3. **Given values:** - $A = 36000$ - Annual interest rate = 0.08 - Monthly interest rate $r = \frac{0.08}{12}$ - Number of periods $n = 70$ 4. **Rearrange the formula to solve for $PMT$:** $$PMT = A \times \frac{r}{(1 + r)^n - 1}$$ 5. **Substitute the values:** $$PMT = 36000 \times \frac{\frac{0.08}{12}}{(1 + \frac{0.08}{12})^{70} - 1}$$ 6. **Calculate intermediate values:** Calculate $r = \frac{0.08}{12} = 0.0066667$ Calculate $(1 + r)^{70} = (1.0066667)^{70}$ 7. **Evaluate $(1.0066667)^{70}$:** $$ (1.0066667)^{70} \approx 1.5657 $$ 8. **Calculate denominator:** $$1.5657 - 1 = 0.5657$$ 9. **Calculate fraction:** $$\frac{r}{(1 + r)^n - 1} = \frac{0.0066667}{0.5657} \approx 0.01178$$ 10. **Calculate $PMT$:** $$PMT = 36000 \times 0.01178 = 424.08$$ **Final answer:** The payment required is approximately $\boxed{424.08}$ per period.