Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 to his savings on the last day of each year. They both earn a 9% rate of return. What is the difference in their savings account balances at the end of thirty years?

A) $35,822.73
B) $36,803.03
C) $38,911.21
D) $39,803.04
E) $40,115.31

Toni is making contributions at the beginning of each period (annuity due), while Tim is making contributions at the end of each period (ordinary annuity). The formula for the future value of an annuity due is $FV=P\times \left(\frac{(1+r{)}^n-1}{r}\right)\times (1+r)$ , and for an ordinary annuity, it is $FV=P\times \left(\frac{(1+r{)}^n-1}{r}\right)$ , where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods.For Toni (annuity due):- $P=\$3,000$ - $r=0.09$ (9% annual interest)- $n=30$ yearsFor Tim (ordinary annuity), the variables are the same but the formula does not include the $(1+r)$ factor at the end.The difference in their savings will be due to the additional year of growth on each of Toni's contributions compared to Tim's. To find the exact difference, calculate the future value for each and subtract Tim's total from Toni's.However, without doing the exact calculation, we know the difference is due to the effect of the first contribution by Toni growing for an extra year for each contribution, which is significant over 30 years at 9% interest. The correct answer is found by applying these formulas or using a financial calculator. Given the options, the correct difference aligns with option B, $36,803.03, which is a result that can be derived from calculating the future values for both scenarios and subtracting them.