Question

Todd and Jessalyn are 25, newly married, and ready to embark on the journey of life.   They both plan to retire 45 years from today. Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $2400 per year to prepare for retirement. Jessalyn just told Todd, though, that she had heard that they would actually have more money the day they retire if they put $2400 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments - than they would have if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do).  

Please help Todd and Jessalyn make an informed decision:   

Assume that all payments are made at the end of a year, and that the rate of return on all yearly investments will be 8.4% annually.

A. How much money will Todd and Jessalyn have in 45 years if they put away $200 per MONTH at the end of each month for the next 45 years? (Remember to adjust the 8.4% annual rate to a Rate per month!) (Round this rate per month to 5 places past the decimal)

                                                                   example of rounding: .062134 = .06213 or 6.213%

B. If Todd and Jessalyn wait 25 years (after the kids are raised!) before they put anything away for retirement, how much will they have to put away at the end of each year for 20 years in order to have $1,000,000 saved up on the first day of their retirement 45 years from today?

Answer 1

रूहानि o formulae used : Solution o future value of an = P / (1+r) - 1 Annuity P 2 = Periodic sate no. layment peld period benodd m mt future value of an amount = Pv/lt. PV 2 money invested today 8 = Annual Interest rate t a number of years E number of periods based on compounding Option. 1 : Invest after lo years, $2400 per year for 3 years Here P. $2400 = 8.4 % = 0.084 n = 35 years 0.084

1 facut 28574.43 .084) 08 - 17. let az (1.084 og both sides Logn z 35 log bose Logo = 35 026350] n z Ant(1.225) x 2 .16.79 --- lii by putting value, we get = 88571-43 [16-79 - 1] =) 98571243 [15.79) = $ 45/19.25 Option 2 Invest for first to years, then - sit for next 35 years. fv at the end of = $2400 0.084 to years •016 & $ 9400 ((1084) 0 - 1 1 0 .084 28571.43 (2.240-1) 2857143 (1.240) - E

सब बाता sit this Now 35 next $ 35428157 it this amout $ 35428-57 for 25 years, Antout of this amonit = will be alter 35 yean go for = 35428.57 (+0.084) = 35428:57 (16-79) (from (1) $594845.69 Chut of option 1 & 2 , Todd &e Jesselyn - should go for option 2, ie. they should I put & 2400 per year away for next to years and simply let that money sit for A next 35 year & they they will get Lo g 594,845-69 % - A when p = $200 monthly g = S = .007 n = 45X12 = 540 t = $ 200 (lot 0.007) S9 - 1 0:007 month 540 = 28.571.42.86 (cloocyjne

takeup - det xa (10007) 540 log both sides legn a 540 log (1.007) = 540 (0.0029) * = Antill 566) X E (36.81~- ( put the above value ini, we get 28571.43( 36-81-1) = $ 1023142-91 Z$10,2 3,143 fr will be $ 10,23143/- f. V. shall be $ 10,00,000 after investing for 20 years after 25 years. from today , Her, we need to calculate the yearly camount, they need to invest for Accumulating & lo 0,ooo after 45 years fv = $ 10,00,000 8 = 0.084 n z 20 years

" fv = o = P {{1+2)" - 1] p [(1-084) - 1 084 -CI 84,000 = p [c1.ose 3 2 -1] - 09 bet x = (1,084) log both sides a z 20 log 7084 - 20(So. 0350) x = Autlog (0.7) = Aut. (0.7) 5012' --.ciis this value in , we get i 84000 = P [5.0/2 - 1] 84000 a P (4.012) e = 84000/4.012 - $ 20,937.1884 = $ 20937./- They have to invest $ 20,937 - each Syear for 20 years for alle & roogoool-