Question

you just won a lottery entitling you to receive, starting today, a series of 21 quarterly payments of 25,000 each, followed, one year after this series of payments end, by a second series of annual payments of $30,000 each forever! (This $30,000 payment is to be recieved exactly one year after the last $25,000 payment is received) if the appropriate discount rate is =10% compounded continuously, what is the present value of all these future lottery payments?

please show how the problem has been solved algebraically

Answer 1

EAR =[ e^(Annual percentage rate) -1]*100

10=(e^(APR%/100)-1)*100

APR% = 9.531

PVAnnuity Due = c*((1-(1+ i/100)^(-n))/i)*(1 + i/100 )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 25000*((1-(1+ 9.531/100)^-21)/(9.531/100))*(1+9.531/100)

PV = 244834.0915

Using Calculator : Press buttons : "2ND"+"PMT"+"2ND"+"ENTER"+"2ND"+"CPT" then assign

PMT =25000

I/Y =9.531

N =21

FV = 0

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(9.531/(100),21,,PV,1)

PV of perpetual CF = Perpetual CF/(interest rate)

PV of perpetual CF = 30000/(0.09531)

PV of perpetual CF = 314762.3544

Future value = present value*(1+ rate)^time

314762.3544 = Present value*(1+0.09531)^20

Present value = 50961.44

Using Calculator: press buttons "2ND"+"FV" then assign

FV =-314762.3544

I/Y =9.531

N =20

PMT = 0

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(0.09531,20,,314762.3544,)

Total = 50961.44+244834.0915

=

295795.53