Question

please reply with only the number answer to the underlined question. i do not want to see any other equations or numbers. just the answer to the underlined questions. thank you.

Question 5 1 pts Your clients want help figuring out how much they need to save each month so that they can reach their retirement goal. If your clients are currently 37 years old and want to retire when they are age 63, how much do they need to save at the end of each month to reach their goal? They currently have $130,000 saved for retirement. Assume the following: • Your clients currently spend $80,000 (in today's dollars), and they want to spend 100% of that in retirement • General inflation is about 2.9% per year • Your clients can earn an annual rate of return of 7.9% on their investments • Your clients are both the same age and want to retire at the same age • You estimate that your clients' planning horizon should be until age 95 • Your clients don't plan on leaving any money to their children when they die

Answer 1

Answer: Amount to be saved every month is $21,447.60

(For reference):

Time to retire (n) = 63-37 years= 26 years. Inflation rate (i)= 2.9%. Present spending= $80,000. Interest rate (r)=7.9%

Current savings= $130,000. Future Value of Current Savings on retirement= $130,000*(1+r)^n = $938,644.01

First payment after retirement= $80,000*(1+i)^n = $80,000*(1.029)^26= $80,000*2.102809 = $168,224.69

Life expectancy after retirement= 95-63 years= 32 years

PV of growing annuity with first PMT of the above amount= $2,627,395.36

Details as follows:

C D B 1 Present Value of Annuity Payments at the end of each period 2 3 Present value of growing annuity is calculated using the formula PVA=[P/(r-g)]*(1-[(1+g)/(1+r)^n]} 4 Where P= First payment, 5 n= Number of payments. 6 r=Rate of interest per period in decimals and g= Growth rateper period in decimals 7 All amounts in $ 8 Given that 9 First payment (P)= 168224.69 No. of years (N)= 10 Rate of interest (% p.a)=R= 7.9 No. of payments a year (t)= 11 Growth rate (% p.a.)=G= 2.9 12 13 Calculations: 14 Formula Cell reference 15 Interest rate per period in decimals (r )= R/(100*t) D10/(100*G10) 16 No. of periods (n)= N*t G9*G10 17 Growth rate (g) G/(100*t) D11/(100*G10) [(1+g)/(1+r)^n ((1+G17)/(1+G15)) ^G16 19 1-[(1+g)/(1+r)^n 1-G18 G15-G17 P/(r-g) D9/20 22 Present value of growing annuity PV= [P/(r-g)]*{1-[(1+g)/(1+r)^n]} G21*G19 Rounded to 18 Value 0.079 32 0.029 0.219081529 0.780918471 0.05 3364493.8 2627395.355 $2,627,395.36 20 24

Net corpus required to be built till retirement= $2,627,395.36- $938,644.01 = $1,688,751.35

Amount required to be saved every month till retirement=$21,447.60

Details as follows:

1 Annuity Payment Payments at the end of each period 3 Amount of periodical payments is calculated using the formula PMT= (PV*r)/(1-(1+r)^-n] 4 Where PMT= Periodical payments required, 5 PV= Present value of future sum which is FV/(1+r)^n 6 n= Number of payments. 7 r= Rate of interest per period in decimals All amounts in $ Given that 10 Future value required FV= 1688751.35 No. of years (N) 11 Rate of interest (% p.a)=R= 7.9 No. of payments a year (t) 12 13 Calculations: 14 Formula Cell reference Value 15 Interest rate per period in decimals (r )= R/(100*t) D11/(100*G11) 0.079 16 No. of periods (n)= N*t O'G11*G11 26 17 (1+r)= 1+G15 1.079 18 (1+r)^n= G174G16 7.220338556 19 Present Value of future amount (PV)= FV/(1+r)^n= D10/G18 233888.1116 (1+r)^-n= G174-G16 0.138497661 [1-(1+r)^-n]= 1-G20 0.861502339 FV*r= G19*G15 18477.16082 23 Periodical payment required (PMT)= (FV*r)/(1-(1+r)^-n] G22/G21 21447.60377 Rounded to $21,447.60