Question

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

Question 2 1 pts You estimate that for their first year of retirement, your clients will need to spend about $100,000 in future dollars. With this goal in mind, how much in total will your clients need to have saved by the time they retire? Assume the following: • General inflation is about 3.0% per year • Your clients can earn an annual rate of return of 7.7% on their investments during retirement Your clients are both the same age and want to retire at age 66 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

The amount to be saved by the time they retire is $1,544,313.52

(For reference only):

This amount is arrived at as the present value of growing annuity for 29 years (ie.,.95-66 years) with inflation as growth rate as follows:

7 B C D 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 All amounts in $ Given that 9 First payment (P)= 100000 No. of years (N)= 10 Rate of interest (% p.a)=R= 7.7 No. of payments a year (t)= 11 Growth rate (% p.a.)=G= 12 13 Calculations: 14 Formula Cell reference Value 15 Interest rate per period in decimals (r )= R/(100*t) D10/(100*G10) 0.077 16 No. of periods (n)= N*t G9*G10 29 17 Growth rate (g) G/(100*t) D11/(100*G10) 0.03 18 [(1+g)/(1+r)^n ((1+G17)/(1+G15))^G16 0.274172644 1-[(1+g)/(1+r)^n 1-G18 0.725827356 20 G15-G17 0.047 P/(r-g) D9/G20 2127659.574 22 Present value of growing annuity PV= (P/(r-g)]*(1-[(1+g)/(1+r)^n]} G21*G19 1544313.523 23 Rounded to $1,544,313.52 19 21