PV & FV Calculations

Question

Your best friend Frank just celebrated his 30th birthday and wants to start saving for his anticipated retirement. Frank plans to retire in 35 years and believes that he will have 20 good years of retirement and believes that if he can withdraw $90,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Frank for all scenarios presented below is 8% per year.  This is an annual rate, review each individual question for more specifics on compounding periods per year.

Because Frank is planning ahead, the first withdrawal will not take place until one year after he retires. he wants to make equal annual deposits into his account for his retirement fund.      

                           

Questions; - CAN YOU PLEASE TELL MW HOW TO SOLVE THESE QUESTIONS USING A FINANCIAL CALCULATOR?

A.    If he starts making these deposits in one year and makes his last deposit on the day he retires, what amount must he deposit annually to be able to make the desired withdrawals at retirement?

A1) First: Amount needed at retirement (3 pts):

Answer 1

There are two things to be calculated here:

1. The amount that needs to be in the account when Frank finishes working and;
2. The amount needed to be deposited each period to reach that total amount in #1 (the answer you seek)

To find #1 using the calculator, the following inputs need to be entered in the NPV screen. I've recorded a video on this here, but I'm assuming you know how to get into the NPV entry screen: https://www.youtube.com/watch?v=j4d6gbJugF8

N = 20 (years in retirement)

I = 8% (given in problem)

PMT = $-90,000 (His annual withdrawal amount)

FV = $0 (when Frank dies, he wants nothing in savings)

PV = (BLANK -> this is what you solve for)

Period = END (he takes the money out at the end of the period)

Doing the above you should receive: --> Part #1

Now, we can set up part #2 knowing the desired amount:

N = 35 (years til retirement)

I = 8% (Given rate)

FV = 883,633.27

PV = $0 (nothing in the amount now)

PMT = (LEAVE BLANK --> This is what you are seeking)

Period = END

Doing the above you should receive: --> Part #2...your answer

Answer 2

This is a multistep process. Frank wants a stream of 90,000 for 20 years So we need to know the present value of a stream of 20 90,0000 payments discounted at 8%.

Presnet Value= Payment*(payment multiplier)

The payment multiplier is

PM(N,i) = (1/i)(1-(1/1(1+i))^N) which = (1/.08)*(1-(1/1.08))^20) =(.78545)/.08)=9.81815.

So, PV= 90,000*9.81815 or PV = = 883,633.5.

That seems like a lot of money to accumulate. Never fear, the miracle of Compound interest is Here. He will need 833,633.5 in 35 years. How much would we have to put in the bank today at 8% to have that amount in 35Years? The answer is (bang the cymbals) PV(today)(1+8%)^³⁵= PV 35 years from now.or PV(today) 883,633.5/(1.08%)³⁵= 59,764.15. So if he put that much in the bank today he wouldnt have to go to that financial planner from TD Ameritrade who looks like Matthew Broderick. Hi retirement would be covered.

However we can ask what stream of deposits, made annually , discounted at 8% will have a present value of $59,764.15. Note that if interest rates were zero and always would be he would need 20 years times 90,000 at retirement or 1.8 million dollars. To save 1.8 million dollars in equal installments over 35 years he would have to save 1,800,000/35 per year or 51,428.86 per year. Lets see how much he would have to save with the miracle of compounding

PV =Payment*PM(n,I) = Payment*PM(35,.08) PM(35,.08 = 11.6545 so,

Annual deposit = PV/11.6545 = $5127.96 per year. That is, If you save about 5125 per year for 35 Year and retire with your accumulated savings in a 20 year 8% annuity you will be able to live on 90,000 per year.

Pretty cool huh?

Now using your financial calculator. ( I much rather calculate it out myself as I have a tendency to hit the wrong button and don't know if I made a mistake)

For step 1 enter PMT = 90,000 n = 20 i = .08 calculate PV.

For Step 2 enter 883,633.5 FV, 35 N and i = .08 and calculate PV

Step 3 enter PV= 59,764.15, n= 35 and i= .08 calculate PMT.

If you have any questions on valuing cash flows please reach out to me.