Question

# Assume 360-day year and 30-day month in your analysis Salary scalar 3.33 Your clients, both just...

Assume 360-day year and 30-day month in your analysis Salary scalar 3.33 Your clients, both just turned 40, will retire when they turn 62. They have a current salary at an annual rate of (\$10,000*salary scalar + \$100,000), being paid equally at the end of each month. They expect a 3% raise in their salary every year until they retire. They deposit 12% of their monthly salary in their 401(k) account that generates an annual rate of return of 10%, compounded daily. In addition, their employer matches their contribution with 5% of their monthly salary to the same 401(k) account. 1. Determine the cash flows pattern of the monthly contributions to the 401(k) account within each year; and calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER, used in your analysis. Also, calculate the yearend value of the 401(k) contributions for each year. Verify your work for Years 1 and 2 only with either the formula or the financial calculator approach! 2. Determine the pattern of the year-end values of the 401(k) contributions across years; and calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER, used in your analysis. Also, calculate their 401(k) account balance upon their retirement.

 Current Annual Salary \$133,300 (10000*3.33+100000) 133300 Next years Annual Salary \$137,299 (133300*1.03) Salaty in year (n+1)=1.03*Salary in year(n) Interest rate: 10% compounded daily Effective annual Rate=r (1+r)=(1+(0.1/365))^365 1+r= 1.105155782 r= 0.105155782 Monthly rate=i (1+i)^12=1.105155782 1+i=(1.105155782^(1/12))= 1.008367001 Monthly interest rate =i= 0.008367001 (Using Excel FV Function with Number of years of savings 22 (62-40) Rate=0.008367001, Nper=12,Pmt=E N A B=A/12 C=B*0.12 D=B*0.05 E=C+D F G=F*(1.105155782^(22-N)) Year Annual Salary Monthly Salary Deposit in 401(k) Employer Total Year End Value Value of Yearly Match Savings Saving at retirement 1 \$133,300 \$11,108 \$1,333 \$555 \$1,888 \$23,733.46 \$                                   193,756 2 \$137,299 \$11,442 \$1,373 \$572 \$1,945 \$24,445.47 \$                                   180,579 3 \$141,418 \$11,785 \$1,414 \$589 \$2,003 \$25,178.83 \$                                   168,299 4 \$145,661 \$12,138 \$1,457 \$607 \$2,064 \$25,934.20 \$                                   156,854 5 \$150,030 \$12,503 \$1,500 \$625 \$2,125 \$26,712.22 \$                                   146,187 6 \$154,531 \$12,878 \$1,545 \$644 \$2,189 \$27,513.59 \$                                   136,246 7 \$159,167 \$13,264 \$1,592 \$663 \$2,255 \$28,339.00 \$                                   126,980 8 \$163,942 \$13,662 \$1,639 \$683 \$2,323 \$29,189.17 \$                                   118,345 9 \$168,860 \$14,072 \$1,689 \$704 \$2,392 \$30,064.84 \$                                   110,297 10 \$173,926 \$14,494 \$1,739 \$725 \$2,464 \$30,966.79 \$                                   102,796 11 \$179,144 \$14,929 \$1,791 \$746 \$2,538 \$31,895.79 \$                                     95,806 12 \$184,518 \$15,377 \$1,845 \$769 \$2,614 \$32,852.67 \$                                     89,291 13 \$190,054 \$15,838 \$1,901 \$792 \$2,692 \$33,838.25 \$                                     83,218 14 \$195,756 \$16,313 \$1,958 \$816 \$2,773 \$34,853.39 \$                                     77,559 15 \$201,628 \$16,802 \$2,016 \$840 \$2,856 \$35,898.99 \$                                     72,285 16 \$207,677 \$17,306 \$2,077 \$865 \$2,942 \$36,975.96 \$                                     67,369 17 \$213,907 \$17,826 \$2,139 \$891 \$3,030 \$38,085.24 \$                                     62,788 18 \$220,325 \$18,360 \$2,203 \$918 \$3,121 \$39,227.80 \$                                     58,518 19 \$226,934 \$18,911 \$2,269 \$946 \$3,215 \$40,404.63 \$                                     54,538 20 \$233,742 \$19,479 \$2,337 \$974 \$3,311 \$41,616.77 \$                                     50,829 21 \$240,755 \$20,063 \$2,408 \$1,003 \$3,411 \$42,865.28 \$                                     47,373 22 \$247,977 \$20,665 \$2,480 \$1,033 \$3,513 \$44,151.24 \$                                     44,151 SUM \$                               2,244,066 Total Amount at retirement \$                      2,244,066

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