You plan to make 5 equal annual deposits into an account paying 5% interest. The

Question

You plan to make 5 equal annual deposits into an account paying 5% interest. The first deposit is to be made today. You want to turn the account over to your school and have enough money in the account such that they will be able to withdraw from the account 50,000 per year in perpetuity( first withdrawal to be made in 2025)
a.how large must be your five original deposits be?
b. Now suppose that you make only the first four deposits (using the value found in part a.) You skip the fifth deposit . But feel bad, you make a deposit in 2019, and a another deposit in 2020(both of theses deposits are also the size found in part a) how much will your school be able to withdrawal from the account in perpetuity if the college still wants to begin withdrawing the funds in the year 2025?

How do you do this on a calculator?

Explanation / Answer

Year 2011 is start year.

i = 5%

Value of Perpetuity VP at T=15 is = A/i = 50000/5% = $1,000,000

So PV of VP at t5 ie (15-5=10yrs)= VP/(1+i)^10 = 1000000/(1+5%)^10 = $613,913

So FV of 5 Equal deposit from T0 to t4 is $613,913.

ie FV of Annuity for n=5 at i=5% is $613,913 and we need to find PMT

Using excel function PMT, we have PMT=PMT(Rate,nper,pv,fv,[type])

ie PMT = PMT(5%,5,0,-613913,1)...Note type =1 as First deposit is at t=0

ie PMT = $105,812

So we need to make 5 equal payments of $105,812 each.........Ans (a)

b. FV of annuity for nper=4, PMT= $105,812, i=5% is FV=FV(rate,nper,PMT,(pv),[type])

ie FVA = FV(5%,4,-105812,,1) = $478,866 ..Ths is at t4

SO FV = PV*(1+i)^n

So at t25 ie after 15-4 = 11yrs, FV= $478,866*(1+5%)^11= $819,023 ....(B)

Depsoit at t19 is invested for 25-19 = 6yrs

So FV = 105812*(1+5%)^6 = $141,798 .....(C)

Depsoit at t20 is invested for 25-20 = 5yrs

So FV = 105812*(1+5%)^5 = $135,046 ..... (D)

So lump sum at t25 = B+C+D = $1,095,867

So Amt withdrawalble = VP*i = $1,095,867*5% = $54,793 ....Ans

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