1. **Stating the problem:** We want to find the monthly payment that the parents will receive if the house is sold in 7 years for 3.2 million, with an interest rate of 8.06% compounded monthly. Then, we need to find how many siblings must pay the monthly amount of 6700 each to reach this goal. Finally, if only 3 children pay 6700 monthly, determine the future value they can accumulate in 7 years. 2. **Calculate the monthly interest rate:** $$ i = \frac{8.06\%}{12} = 0.0806 / 12 = 0.006717 $$ 3. **Calculate the total number of payments:** $$ n = 7 \times 12 = 84 $$ 4. **Find the monthly payment $P$ needed to accumulate $3,200,000$ in 7 years at monthly interest $i$ and $n$ payments using the future value of an annuity formula:** $$ FV = P \times \frac{(1+i)^n - 1}{i} $$ Rearranged for $P$: $$ P = FV \times \frac{i}{(1+i)^n - 1} $$ Plug in values: $$ P = 3200000 \times \frac{0.006717}{(1+0.006717)^{84} - 1} $$ Calculate $(1+0.006717)^{84}$: $$ (1.006717)^{84} \approx 1.747 $$ Calculate denominator: $$ 1.747 - 1 = 0.747 $$ Calculate numerator: $$ 3200000 \times 0.006717 = 21494.4 $$ Calculate $P$: $$ P = \frac{21494.4}{0.747} \approx 28775.36 $$ So, the parents receive roughly $28775.36$ per month total. 5. **Calculate the number of siblings needed if each can pay $6700$ per month:** $$ \text{siblings} = \frac{28775.36}{6700} \approx 4.29 $$ Since siblings must be a whole number and meet or exceed this, the answer is 5 siblings. 6. **Calculate how much 3 children paying $6700$ monthly can accumulate in 7 years:** Total monthly payment from 3 children: $$ 3 \times 6700 = 20100 $$ Use future value of annuity formula: $$ FV = P \times \frac{(1+i)^n - 1}{i} $$ Already know: $$ (1+i)^n - 1 = 0.747,\quad i=0.006717 $$ Calculate $FV$: $$ FV = 20100 \times \frac{0.747}{0.006717} = 20100 \times 111.257 \approx 2236493 $$ **Final answers:** - Parents receive about $28775.36$ per month total. - Exactly $5$ siblings needed paying $6700$ each. - Three siblings paying $6700$ each can offer about $2,236,493$ after 7 years.