Question

Sally Mander wants to set up a perpetual annuity for herself that will pay $80,000 annually that will begin 40 years from now. Assuming an interest rate of 7% and with the impact of inflation of 3%. how much will Sally need to save annually? $8,045 $9,047 $10,018 $11.051

Answer 1

Factoring inflation of 3%, present value of the perpetual annuity of $80,000 with inflation of 3% is $2,000,000 arrived at as follows:

C D 1 Present Value of Annuity 7 3 Present value of perpetual cash flow is calculated using the formula PV=P/(r-g) 4 Where P= Periodical payments, 5 r= Rate of interest per period in decimals 6 g=growth rate in decimals All amounts in $ Given that 9 Periodical payments (P)= 80000 Growth rate per year-inflation (%) 10 Rate of interest (% p.a)=R= 7 No. of payments a year (t)= 11 12 Calculations: Formula Cell reference Value 14 Interest rate per period in decimals (r)= R/(100*t) D10/(100*G10) 0.07 15 Growth rate in decimals G/(100*t) G9/(100*G10) 0.03 16 Present value of perpetual cash flow PV= P/(r-g) D9/1G14-G15) 2000000 Rounded to $2,000,000.00 10 13

Amount required to be invested every year, for 40 years is $10,018 arrived at as follows:

B G C D Payments at the end of each period 1 Annuity Payment 8 1 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= 2000000 No. of years (N) 40 11 Rate of interest (% p.a)=R= 7 No. of payments a year (t) 12 13 Calculations: Formula Cell reference 15 Interest rate per period in decimals (r)= R/(100*t) 011/(100*G11) 0.07 16 No. of periods (n)= N*t O'G11*G11 40 17 (1+r)= 1-G15 1.07 18 (1+r)^n= G174G16 14.97445784 19 Present Value of future amount (PV)= FV/(1+r)^n= D10/18 133560.762 (1+r)^-n= G174-G16 0.066780381 [1-(1+r)^-n]= 1-G20 0.933219619 FV*r= G19*G15 9349.253342 23 Periodical payment required (PMT)= (FV*r)/(1-(1+r)^-n] G22/G21 10018.27775 Rounded to $10,018.28 14 20