Question

720 740 80 62 44 26 14 1 0 0 0 0 0
740 760 83 65 47 28 16 3 0 0 0 0 0
760 780 86 68 50 31 18 5 0 0 0 0 0
780 800 89 71 53 34 20 7 0 0 0 0 0
800 820 92 74 56 37 22 9 0 0 0 0 0
820 840 95 77 59 40 24 11 0 0 0 0 0
840 860 98 80 62 43 26 13 1 0 0 0 0
social security tax that is 6.2% of her gross pay
medicare tax that is 1.45% of her gross pay
state tax that is 21% of her federal tax
determine how marilyns net pay will be affected if she increases her federal withholding allowances from 3 to 4.
a. her net pay will increase by $15.00.
b. her net pay will decrease by $15.00.
c. her net pay will increase by $18.15.
d. her net pay will decrease by $18.15.

Explanation:

Step1: Find federal tax change

First, identify federal tax for 3 allowances and 4 allowances. From the table, for gross pay bracket $840-860$, federal tax is $43$ (3 allowances) and $26$ (4 allowances).
Change in federal tax: $26 - 43 = -17$ (tax decreases by $17$)

Step2: Calculate Social Security tax change

Social Security tax is 6.2% of gross pay. Since gross pay doesn't change, this tax is unchanged: $\Delta SS = 0$

Step3: Calculate Medicare tax change

Medicare tax is 1.45% of gross pay. Gross pay is unchanged, so this tax is unchanged: $\Delta Med = 0$

Step4: Calculate state tax change

State tax is 21% of federal tax. Change in state tax: $0.21 \times (-17) = -3.57$ (state tax decreases by $3.57$)

Step5: Calculate total net pay change

Net pay change = - (total tax change) = -($-17 -3.57$) = $17 + 3.57 = 20.57$? Correction: Wait, recheck table row. Wait, let's use correct row: When allowances go from 3 to 4, let's take gross pay as, say, $850$ (mid of 840-860). Federal tax for 3 allowances is 43, 4 allowances is 26. So federal tax decreases by $17$. State tax is 21% of federal tax, so state tax decreases by $0.21*17 = 3.57$. Total tax decrease = $17 + 3.57 = 20.57$? No, wait, no: Net pay increases by total tax decrease. Wait, but the options are 15, 15, 18.15, 18.15. Wait, wrong row: Let's check the row for gross pay 780-800? No, wait, the question is about increasing allowances from 3 to 4. Wait, let's take the correct column: The columns are number of allowances: 0,1,2,3,4,5,... Wait, no, the first row after gross pay: 80 (0 allowances), 62 (1), 44 (2), 26 (3), 14 (4)? No, wait, the columns are: gross pay start, gross pay end, then 0 allowances,1,2,3,4,5,6,7,8,9,10. Oh right! So for a given gross pay, 3 allowances is column 5, 4 allowances is column 6. Let's take Marilyn's gross pay: Let's assume her gross pay is in the 840-860 bracket. 3 allowances: 43, 4 allowances:26. Federal tax decrease: 43-26=17. State tax is 21% of federal tax, so state tax was 0.21*43=9.03, now 0.21*26=5.46, so state tax decreases by 9.03-5.46=3.57. Social Security and Medicare are based on gross pay, so no change. Total decrease in taxes:17+3.57=20.57? No, this doesn't match options. Wait, maybe gross pay is 760-780: 3 allowances is 31, 4 allowances is18. Federal tax decrease:13. State tax decrease:0.21*13=2.73. Total tax decrease:13+2.73=15.73? No. Wait 800-820: 3 allowances 34, 4 allowances20. Federal decrease 14. State decrease 0.21*14=2.94. Total 16.94. 780-800: 31-18=13, 13+2.73=15.73. 740-760: 28-16=12, 12+2.52=14.52. 820-840: 40-24=16, 16+3.36=19.36. 840-860: 43-26=17, 17+3.57=20.57. Wait, the options have 18.15. Oh! Wait, I messed up: Social Security and Medicare are deductions, but when federal withholding decreases, gross pay is same, so SS and Medicare are same. Wait, no: Net pay = Gross pay - (Federal tax + State tax + SS + Medicare). So change in net pay = - (change in Federal tax + change in State tax). Change in Federal tax is (new federal - old federal) = 26-43=-17. Change in State tax is 0.21*(26-43)=0.21*(-17)=-3.57. So total change in deductions: -17-3.57=-20.57. So net pay change = -(-20.57)=20.57. But this isn't an option. Wait, wait, maybe the tax table is federal withholding, and the question is that increasing allowances from 3 to 4: Let's check the column for 3 allowances and 4 allowances in the same row. Wait, maybe the gross pay is $790$? No, wait, maybe I misread the tax rates: Social Security is 6.2% of gross pay, Medicare 1.45%, state tax 21% of FEDERAL tax, not gross. Wait, another approach: The change in net pay is equal to the increase from lower federal tax minus the lower state tax (since state tax is 21% of federal). So if federal tax goes down by X, state tax goes down by 0.21X, so net pay goes up by X + 0.21X = 1.21X. Now, which X gives 1.21X=18.15? X=18.15/1.21=15. So X=15. So federal tax decreases by $15$. So find where 3 allowances minus 4 allowances is 15. Looking at the table: 44-29? No, 50-35? No, 53-38? No, 56-41? No, 59-44? No, 62-47=15. Oh! 62 (3 allowances) and 47 (4 allowances) in the 740-760 row? No, 740-760: 3 allowances is 28, 4 is16: 12 difference. Wait 80 (0),62(1),44(2),26(3),14(4): 26-14=12. 83(0),65(1),47(2),28(3),16(4):28-16=12. 86(0),68(1),50(2),31(3),18(4):31-18=13. 89(0),71(1),53(2),34(3),20(4):34-20=14. 92(0),74(1),56(2),37(3),22(4):37-22=15. Ah! Here: 3 allowances is 37, 4 allowances is22. Difference is 15. So X=15. Then net pay increase is 15 + 0.21*15=15+3.15=18.15. Yes! That's option c. So gross pay is in 800-820 bracket.

Step6: Confirm net pay change

Net pay increases by the total reduction in taxes: $15 + (0.21×15) = 15 + 3.15 = 18.15$

Answer:

c. Her net pay will increase by $18.15$.