You are planning to save for your retirement in 35 years and the college tuition
ID: 2818697 • Letter: Y
Question
You are planning to save for your retirement in 35 years and the college tuition for your two children. Your current monthly salary is $9,000 per month and you expect your salary to keep pace with inflation. You expect inflation to be a 3.5 percent EAR for the rest of your life. You plan to deposit 12 percent of your salary each month into a retirement account. Additionally, your employer will deposit 4 percent of your salary into the account. You expect to earn a 10.8 nominal nominal EAR in your retirement savings account until retirement. Your children will begin college 15 years and 17 years from now. The university that you plan for your children to attend has started a new legacy program where for a minimal donation today, the school will guarantee that the tuition for your first child will be $130,000 and the tuition for your second child will be $135,000. Each of these tuition payments will be made when your child starts college and will cover the entire four years of tuition. If you can earn an 8.7 percent EAR after you retire, how much can you withdraw each month in real terms for the 25 years of your retirement?
Explanation / Answer
We need to calculate future value of this fund 35 years from now. Annual salary at beginning is 9000*12 = 108,000 and this will grow at the rate of 3.5% Year Salary Contribution to fund @ 12% Employer Contribution @ 4% Total Contribution Expected outflow Net Contribution/Withdrawal Rate of Interest Discounting Factor Future Value 1 108,000 12,960 4,320 17,280 - 17,280 10.80% 32.69 564,801 2 111,780 13,414 4,471 17,885 - 17,885 10.80% 29.50 527,590 3 115,692 13,883 4,628 18,511 - 18,511 10.80% 26.62 492,830 4 119,742 14,369 4,790 19,159 - 19,159 10.80% 24.03 460,360 5 123,932 14,872 4,957 19,829 - 19,829 10.80% 21.69 430,029 6 128,270 15,392 5,131 20,523 - 20,523 10.80% 19.57 401,697 7 132,760 15,931 5,310 21,242 - 21,242 10.80% 17.66 375,231 8 137,406 16,489 5,496 21,985 - 21,985 10.80% 15.94 350,509 9 142,215 17,066 5,689 22,754 - 22,754 10.80% 14.39 327,416 10 147,193 17,663 5,888 23,551 - 23,551 10.80% 12.99 305,845 11 152,345 18,281 6,094 24,375 - 24,375 10.80% 11.72 285,694 12 157,677 18,921 6,307 25,228 - 25,228 10.80% 10.58 266,871 13 163,195 19,583 6,528 26,111 - 26,111 10.80% 9.55 249,289 14 168,907 20,269 6,756 27,025 - 27,025 10.80% 8.62 232,864 15 174,819 20,978 6,993 27,971 130,000 (102,029) 10.80% 7.78 (793,448) 16 180,938 21,713 7,238 28,950 - 28,950 10.80% 7.02 203,191 17 187,270 22,472 7,491 29,963 135,000 (105,037) 10.80% 6.33 (665,360) 18 193,825 23,259 7,753 31,012 - 31,012 10.80% 5.72 177,299 19 200,609 24,073 8,024 32,097 - 32,097 10.80% 5.16 165,617 20 207,630 24,916 8,305 33,221 - 33,221 10.80% 4.66 154,706 21 214,897 25,788 8,596 34,384 - 34,384 10.80% 4.20 144,513 22 222,419 26,690 8,897 35,587 - 35,587 10.80% 3.79 134,992 23 230,203 27,624 9,208 36,833 - 36,833 10.80% 3.42 126,098 24 238,260 28,591 9,530 38,122 - 38,122 10.80% 3.09 117,790 25 246,599 29,592 9,864 39,456 - 39,456 10.80% 2.79 110,030 26 255,230 30,628 10,209 40,837 - 40,837 10.80% 2.52 102,780 27 264,164 31,700 10,567 42,266 - 42,266 10.80% 2.27 96,009 28 273,409 32,809 10,936 43,745 - 43,745 10.80% 2.05 89,683 29 282,979 33,957 11,319 45,277 - 45,277 10.80% 1.85 83,775 30 292,883 35,146 11,715 46,861 - 46,861 10.80% 1.67 78,255 31 303,134 36,376 12,125 48,501 - 48,501 10.80% 1.51 73,099 32 313,743 37,649 12,550 50,199 - 50,199 10.80% 1.36 68,283 33 324,724 38,967 12,989 51,956 - 51,956 10.80% 1.23 63,784 34 336,090 40,331 13,444 53,774 - 53,774 10.80% 1.11 59,582 35 347,853 41,742 13,914 55,656 - 55,656 10.80% 1.00 55,656 Future Value of Fund 5,917,362 This will be the total fund amount at retirement for which we need to withdraw each month for 25 years I.e. 25*12 = 300months Nominal interest rate for this fund is 8.7% and inflation is 3.5% which means real interest rate is 5.2% Monthly interest rate will be 5.2/12 = 0.433% Now, using Financial calculator we will out :- PV - 5,917,362 FV - 0 N - 300 I/Y 0.43% Compute PMT ($35,271.39)
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