Question

In: Finance

Your aunt has $780,000 invested at 5.5%, and she now wants to retire. She wants to...

Your aunt has $780,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?

Solutions

Expert Solution

Given: AMount having today = 780000, Annutiy= 45000 beginning today,rate 5.5%, FV left with 50000.

Find no. of years .

If you having finanial calculator then put values in TVM as after get on with BGN mode

I/Y=5.5,PV= - 780000, PMT=45000, FV= 50000 compute N= 42.58 years Approx

If not having financial calculator then use Trial and error method. Use any approx no. as time and calculate the present value Like assume time 10,20,30,40 and calculate PV.

Assume time 40 years, Now calculate PV

PV= Annuity + Annuity x cumulative discounting factor @ 5.5% for 40 years + FV/(1+0.055)40

To calculate the Cumulative discounting factor you need excel or can calculate on calculator as 100/105.5 = 0.947867298 and mutiply this with itself 39 more times]

PV = 45000 + (45000 x 16.046124) + 50000/8.513308

PV = 45000 + 722075.59 + 5873.16

PV = 772948.75

You fall little short to reach 780000. So now try for 45 years.  

PV= Annuity + Annuity x cumulative discounting factor @ 5.5% for 45 years + FV/(1+0.055)45

To calculate the Cumulative discounting factor you need excel or can calculate on calculator as 100/105.5 = 0.947867298 and mutiply this with itself 44 more times]

PV = 45000 + (45000 x 16.547725) + 50000/11.12655

PV = 45000 + 744647.63 + 4493.76

PV = 794141.39

So you exeed 780000. So our answer lies in between 40 to 45 years and for this Do interpolation:

= 45 - ( 0.667278 x 5)

= 45 - 3.3363

= 41.66 year approx

As you can see with finanial calculator you get exact result = 42.58 year and with 2nf method resuly is near approximation= 41.67 year  


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