Final answer:
The question involves calculating the difference in Saul's retirement savings if he started investing at age 20 instead of at age 30, using monthly compounding and an annual rate of 3.5%. By finding the future values for both starting points and subtracting them, we can determine how much more he'd have accumulated.
Step-by-step explanation:
The student's question revolves around determining how much more Saul would have in his retirement savings if he began investing at age 20 instead of at age 30, with a monthly investment of $425 and an annual return rate of 3.5%, compounded monthly. To solve this, we'll calculate the future value of Saul's investment for both scenarios (starting at 20 and at 30) and then find the difference.
Starting at Age 20:
Future Value = P × ¶(¶(1 + r/n)^(nt) - 1) / (r/n)
Where:
P = monthly investment = $425
r = annual interest rate = 3.5% or 0.035
n = number of times the interest is compounded per year = 12
t = number of years the money is invested = 40 (from age 20 to 60)
Starting at Age 30:
Using the same formula but with t = 30 (from age 30 to 60).
Once we have both future values, we subtract the future value of starting at age 30 from the future value of starting at age 20 to find the difference, which would be the additional amount Saul would have had he started investing 10 years earlier.