Use the following information for all following questions unless they specify otherwise: Estimated inflation: 3% Estimated general US stock market return: 10% Estimated general US bond market return: 6% As a reminder, we have so far the following formulas: Simple interest: FV=P(1+rt) Compound interest: FV =P(1+r)t Compound interest: PV =FV/(1+r)t Compound interest: (FV/PV)(1/t)=(1+r) Perpetuity: PV=C/r Perpetuity: C=PVr Perpetuity: r=C/PV Growing Perpetuity: PV =C/(rg) \{Watch parenthesis! Growing Perpetuity: C=P(rg) Growing Perpetuity: (rg)=C/PV... So r=(C/PV)+g And g=r(C/PV) Growing Perpetuity: (rg)=C/P Annuity. PV=C/r(C/r)/(1+r)t Annuity: FV=(C/r)(1+r)t(C/r) Annuity Due PV: (1+r) Annuity PV =(1+r)(C/r(C/r)/(1+r)t} Annuity: C =PV/{1/r(1/r)/(1+r)t} Annuity: C=FV/{(1/r)(1+r)t(1/r)} Growing Annuity: PV =C1/(rg)(C2/(rg))/(1+r)t where C2=(1+g)t * C1 Growing Annuity: PV =C/(rg){C/(rg)}{(1+g)/(1+r)}t \{Put all together\} Growing Annuity FV =(1+r)t * \{Growing Annuity PV\} Growing Annuity FV ={C/(rg)}(1+r)t{C/(rg)}(1+g)t Growing Annuity C= PV /(1/(rg){1/(rg)}({(1g)/(1r)}t} Growing Annuity C =FV/{1/(rg)}x(1+r)){C/(rg)}(1+g)t} 1) Given a set savings pian characterized by the foliowing: 1) Jeff is 45 , 7) pians to retire at 67, 3) expects to llve to 82 4) Currently has 200.000 in savings. 5) invested 80% stock market, 20% bond. 6) JeHf plans to save an additional 10,000 per year, each and every year unte he rotires, again investing at the same 80/20 ratio 7) Once retred Jeff plans on investing at 60% stock and 40% bond Preliminaries: A) What is JeHis NVLE? (Pemaining work life expectancy, aka t1) B) What is JeHi RLE? (Retirement ife expectancy, aia t2) C) What is JeHf s expecied rate of return while working and seving (ri) D) What is JeH expected rate of return whie retiod (r2) E) What will the current 200,000 a avings grow into and become at the sime of retirement, assuming it is continually invested with no tax loss along the way F) What Will the asditional 10,000 per yeer invested, eash and every year until he ratires., become at the time of retirement a) Combining them, how mueh wil Jeft have at the time of retirement? H) If Jeti is interested in a constant income in watirement, what conatant income 0 eoud this retirement aavings purehase as a simpie annuity? 1) If Jet is intereated in a conatant income in retirement, what constant income C could this retirement aavings purehase as an annuty dus instead 3) if JeHt is intereated in an increasing income in retirement, what starting income C couid thia retirement aavings purchase as a prowing annuity whin a JW growth rate (g=.03) ? 10 if JeHt is interested in an increes ng income in retirement, what starting income C could this retirement aavings purenase as a growing annulfy due whth a 31 growth rate (g=03)? L) For answers H.KC find what the initial starng income C is in curremt dollars (Hint: FV = FVI (1+inflationjly where O would be the future value and 1 would be t1) Variations on asove: M) Suppose instead JsH invasted at 10016 stocks whic workeng, repeat IHK with the now change N) Feturn to the originai f1 and the pow stocis and 20% bonds whic woridg and saving: however, now change the retirement savigs pian to 100 sonde. fepeat E-K with this new change. (Hint: E-G should be unchangel) O) Rsturn to the original of and 2 . However, have Jeff Wve to BT. Repeat E-K with this new crange. (Hint: E-G ahould be unchanged) F) Return to the original life expectancy. Now have Jef retire at es irstead of 67 iagain atili iving to az). Repsat E-K with this new cnange. \{Hint: E- S shouid now be changed, as t1 has changedi\} Q) Rsturn to the original problam but have ueff save 43 t more psr year (g04) from ags 45 to 67. Repeat F-L 2) Given a set retirement plan characterized by the following: 8) Jeff ia 45. 9) plans to retire at 67. 10) expecta to live to 82 11) Currently makcea 120,000 12) Calculatea a 80% WFPR 13) Plana to irveat in 100% bonda when retired A) What would Jeff need if retiring right now? B) What would Jeff need in future dollars when retiring? C) What total retirement savings would be needed at the atart of retirement to have this as an annuity paying the exact aame amount each year for all of retirement? D) What total retirement aavinga would be needed at the atart of retirement to heve this as an annuity due paying the exact same amount each year for all of retirement? E) What total retirement aavings would be needed at the start of retirement to have this as an annuity growing 3% per year for all of retirement? \{Not this is not an annuity due\} F) What total retirement savinga would be needed at the atart of retirement to have this as an annuity due growing 3% per year for all of retirement? fNote this is growing and an annuity. due. Easieat to calculate growing and then make the annuity due adjustment\} G) For your anawera in D-F, what conatant annual aavings would be needed to reach this goal. saving the aame amount each and every year until retirement if imveating in 50% atocks and 5096 bonda H) For your answers in D-F, what constant annual aavings would be needed to reach this goal. saving the aame amount each and every year untill retirement if investing in 80%6 stocks and 2096 bonda 1) For your anawers in D-F, what conatant annual aavinga would be needed to reach this goal, aaving the aame amount each and every year until retirement if investing in 100%6 atocks and 0%6 bonds J) For your answera in D-F, what conatant annual savinge would be needed to reach this goal, aaving an amount growing at rate of 456 each and every yegr until retirement if investing in 80% atocica and 20%6 bonds K) For your anawera in D-F, what conatant annual savings would be needed to reach this goal, aaving the aame amount each and every year until retirement if inveating in 80%5 atocks and 2096 bonds if Jeff also had 5100,000 lump sum aavings to atart with at age 45 . To show your anawer firat ahow what that 100,000 would grow into at the atart of retirement L) For your anawers in D-F, what conatant annual aavings would be needed to reach this goal, aaving the same amount each and every year until rebirement if investing in 8056 atocica and 20% bonda if Jeff also wanted to have a cushion of the equivalent of 200,000 in current dollars at the expected life expectancy age of 82. To ahow your anawer firat ahow what that 200,000 in current dollara would be at age 82 . Then diacount that by the appropriate r back to the atart of retirement and show that tote. Then redo D-F including this extra requirement. Use the following information for all following questions unless they specify otherwise: Estimated inflation: 3% Estimated general US stock market return: 10% Estimated general US bond market return: 6% As a reminder, we have so far the following formulas: Simple interest: FV=P(1+rt) Compound interest: FV =P(1+r)t Compound interest: PV =FV/(1+r)t Compound interest: (FV/PV)(1/t)=(1+r) Perpetuity: PV=C/r Perpetuity: C=PVr Perpetuity: r=C/PV Growing Perpetuity: PV =C/(rg) \{Watch parenthesis! Growing Perpetuity: C=P(rg) Growing Perpetuity: (rg)=C/PV... So r=(C/PV)+g And g=r(C/PV) Growing Perpetuity: (rg)=C/P Annuity. PV=C/r(C/r)/(1+r)t Annuity: FV=(C/r)(1+r)t(C/r) Annuity Due PV: (1+r) Annuity PV =(1+r)(C/r(C/r)/(1+r)t} Annuity: C =PV/{1/r(1/r)/(1+r)t} Annuity: C=FV/{(1/r)(1+r)t(1/r)} Growing Annuity: PV =C1/(rg)(C2/(rg))/(1+r)t where C2=(1+g)t * C1 Growing Annuity: PV =C/(rg){C/(rg)}{(1+g)/(1+r)}t \{Put all together\} Growing Annuity FV =(1+r)t * \{Growing Annuity PV\} Growing Annuity FV ={C/(rg)}(1+r)t{C/(rg)}(1+g)t Growing Annuity C= PV /(1/(rg){1/(rg)}({(1g)/(1r)}t} Growing Annuity C =FV/{1/(rg)}x(1+r)){C/(rg)}(1+g)t} 1) Given a set savings pian characterized by the foliowing: 1) Jeff is 45 , 7) pians to retire at 67, 3) expects to llve to 82 4) Currently has 200.000 in savings. 5) invested 80% stock market, 20% bond. 6) JeHf plans to save an additional 10,000 per year, each and every year unte he rotires, again investing at the same 80/20 ratio 7) Once retred Jeff plans on investing at 60% stock and 40% bond Preliminaries: A) What is JeHis NVLE? (Pemaining work life expectancy, aka t1) B) What is JeHi RLE? (Retirement ife expectancy, aia t2) C) What is JeHf s expecied rate of return while working and seving (ri) D) What is JeH expected rate of return whie retiod (r2) E) What will the current 200,000 a avings grow into and become at the sime of retirement, assuming it is continually invested with no tax loss along the way F) What Will the asditional 10,000 per yeer invested, eash and every year until he ratires., become at the time of retirement a) Combining them, how mueh wil Jeft have at the time of retirement? H) If Jeti is interested in a constant income in watirement, what conatant income 0 eoud this retirement aavings purehase as a simpie annuity? 1) If Jet is intereated in a conatant income in retirement, what constant income C could this retirement aavings purehase as an annuty dus instead 3) if JeHt is intereated in an increasing income in retirement, what starting income C couid thia retirement aavings purchase as a prowing annuity whin a JW growth rate (g=.03) ? 10 if JeHt is interested in an increes ng income in retirement, what starting income C could this retirement aavings purenase as a growing annulfy due whth a 31 growth rate (g=03)? L) For answers H.KC find what the initial starng income C is in curremt dollars (Hint: FV = FVI (1+inflationjly where O would be the future value and 1 would be t1) Variations on asove: M) Suppose instead JsH invasted at 10016 stocks whic workeng, repeat IHK with the now change N) Feturn to the originai f1 and the pow stocis and 20% bonds whic woridg and saving: however, now change the retirement savigs pian to 100 sonde. fepeat E-K with this new change. (Hint: E-G should be unchangel) O) Rsturn to the original of and 2 . However, have Jeff Wve to BT. Repeat E-K with this new crange. (Hint: E-G ahould be unchanged) F) Return to the original life expectancy. Now have Jef retire at es irstead of 67 iagain atili iving to az). Repsat E-K with this new cnange. \{Hint: E- S shouid now be changed, as t1 has changedi\} Q) Rsturn to the original problam but have ueff save 43 t more psr year (g04) from ags 45 to 67. Repeat F-L 2) Given a set retirement plan characterized by the following: 8) Jeff ia 45. 9) plans to retire at 67. 10) expecta to live to 82 11) Currently makcea 120,000 12) Calculatea a 80% WFPR 13) Plana to irveat in 100% bonda when retired A) What would Jeff need if retiring right now? B) What would Jeff need in future dollars when retiring? C) What total retirement savings would be needed at the atart of retirement to have this as an annuity paying the exact aame amount each year for all of retirement? D) What total retirement aavinga would be needed at the atart of retirement to heve this as an annuity due paying the exact same amount each year for all of retirement? E) What total retirement aavings would be needed at the start of retirement to have this as an annuity growing 3% per year for all of retirement? \{Not this is not an annuity due\} F) What total retirement savinga would be needed at the atart of retirement to have this as an annuity due growing 3% per year for all of retirement? fNote this is growing and an annuity. due. Easieat to calculate growing and then make the annuity due adjustment\} G) For your anawera in D-F, what conatant annual aavings would be needed to reach this goal. saving the aame amount each and every year until retirement if imveating in 50% atocks and 5096 bonda H) For your answers in D-F, what constant annual aavings would be needed to reach this goal. saving the aame amount each and every year untill retirement if investing in 80%6 stocks and 2096 bonda 1) For your anawers in D-F, what conatant annual aavinga would be needed to reach this goal, aaving the aame amount each and every year until retirement if investing in 100%6 atocks and 0%6 bonds J) For your answera in D-F, what conatant annual savinge would be needed to reach this goal, aaving an amount growing at rate of 456 each and every yegr until retirement if investing in 80% atocica and 20%6 bonds K) For your anawera in D-F, what conatant annual savings would be needed to reach this goal, aaving the aame amount each and every year until retirement if inveating in 80%5 atocks and 2096 bonds if Jeff also had 5100,000 lump sum aavings to atart with at age 45 . To show your anawer firat ahow what that 100,000 would grow into at the atart of retirement L) For your anawers in D-F, what conatant annual aavings would be needed to reach this goal, aaving the same amount each and every year until rebirement if investing in 8056 atocica and 20% bonda if Jeff also wanted to have a cushion of the equivalent of 200,000 in current dollars at the expected life expectancy age of 82. To ahow your anawer firat ahow what that 200,000 in current dollara would be at age 82 . Then diacount that by the appropriate r back to the atart of retirement and show that tote. Then redo D-F including this extra requirement