1. **State the problem:** You want to find the monthly deposit amount needed to reach $1.3$ million in 22 years with an APR of 4% compounded monthly. 2. **Formula used:** The future value of a series of monthly deposits is given by the savings plan formula: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $FV$ is the future value ($1,300,000$), - $P$ is the monthly deposit (what we want to find), - $r$ is the monthly interest rate (APR divided by 12), - $n$ is the total number of deposits (months). 3. **Calculate parameters:** - APR = 4% = 0.04 annually - Monthly interest rate $r = \frac{0.04}{12} = 0.0033333333$ - Number of months $n = 22 \times 12 = 264$ 4. **Rearrange formula to solve for $P$:** $$P = \frac{FV \times r}{(1 + r)^n - 1}$$ 5. **Calculate $(1 + r)^n$:** $$ (1 + 0.0033333333)^{264} = (1.0033333333)^{264} $$ 6. **Calculate numerator and denominator:** $$ (1.0033333333)^{264} - 1 = A $$ 7. **Substitute values:** $$P = \frac{1,300,000 \times 0.0033333333}{A}$$ 8. **Calculate $A$ and then $P$:** Using a calculator, $$ (1.0033333333)^{264} \approx 2.4596 $$ $$ A = 2.4596 - 1 = 1.4596 $$ 9. **Final calculation:** $$P = \frac{1,300,000 \times 0.0033333333}{1.4596} = \frac{4333.3333}{1.4596} \approx 2967.41$$ **Answer:** You should invest approximately **2967.41** each month to reach $1.3$ million in 22 years.