To solve this, we can use the future value of an ordinary annuity formula, which calculates the amount of savings needed to reach a certain future value, given a regular monthly contribution and an interest rate. The formula is:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

Where:

• $FV$ is the future value of the retirement fund, which is $1,733,597.
• $P$ is the monthly contribution (what we are trying to find).
• $r$ is the monthly interest rate.
• $n$ is the number of months the contributions are made.

Step 1: Calculate the variables

• APR (Annual Percentage Rate) = 9.6%, so the monthly interest rate is: $r = \frac{9.6\%}{12} = \frac{0.096}{12} = 0.008$
• Number of months: He will be saving from age 31 to 68, which is 37 years, so: $n = 37 \times 12 = 444 \text{ months}$
• The future value $FV$ is $1,733,597.

Step 2: Solve for $P$ (the monthly contribution)

Rearrange the formula to solve for $P$:

$P = \frac{FV \times r}{(1 + r)^n - 1}$

Substitute the values:

$P = \frac{1,733,597 \times 0.008}{(1 + 0.008)^{444} - 1}$

Now, we can calculate this step by step.

1. Calculate $(1 + 0.008)^{444}$: $(1.008)^{444} = 21.581$
2. Subtract 1: $21.581 - 1 = 20.581$
3. Multiply the future value by the monthly interest rate: $1,733,597 \times 0.008 = 13,868.776$
4. Finally, divide: $P = \frac{13,868.776}{20.581} = 673.91$

It seems there was an error earlier—likely due to misinterpretation of the annuity equation. Let me