1. **Problem statement:** A company needs 113000 in 18 years to replace a computer. They want to make fixed monthly payments into a sinking fund that compounds monthly at an annual interest rate of 6.0%. We need to find the amount of each monthly payment. 2. **Formula used:** The future value of an ordinary annuity (sinking fund) compounded monthly is given by: $$ A = P \times \frac{(1 + r)^n - 1}{r} $$ where: - $A$ is the future value (113000), - $P$ is the monthly payment (unknown), - $r$ is the monthly interest rate, - $n$ is the total number of payments. 3. **Calculate parameters:** - Annual interest rate = 6.0% = 0.06 - Monthly interest rate $r = \frac{0.06}{12} = 0.005$ - Number of years = 18 - Number of monthly payments $n = 18 \times 12 = 216$ 4. **Rearrange formula to solve for $P$:** $$ P = A \times \frac{r}{(1 + r)^n - 1} $$ 5. **Substitute values:** $$ P = 113000 \times \frac{0.005}{(1 + 0.005)^{216} - 1} $$ 6. **Calculate $(1 + 0.005)^{216}$:** $$ (1.005)^{216} \approx 2.996 $$ 7. **Calculate denominator:** $$ 2.996 - 1 = 1.996 $$ 8. **Calculate fraction:** $$ \frac{0.005}{1.996} \approx 0.002505 $$ 9. **Calculate monthly payment $P$:** $$ P = 113000 \times 0.002505 \approx 283.07 $$ **Final answer:** The company should make monthly payments of approximately **283.07** to reach 113000 in 18 years with 6% annual interest compounded monthly.