Question

you recently received an inheritance of $2,000,000 after taxes. You decide to set aside all of that money in a retirement account that pays 5% interest and you plan on making year end contributions of $15,000 for the next 30 years until you reach retirement age. How much should you be able to withdraw at the end of each year of your 20 retirement years?

a. $240,454

b. $482,023

c. $613,639

d. $773,576

Answer 1

The future value of an investment is given as under

Future value = Present value * (1+interest rate)^period

We can use excel function =FV to calculate future value of these investments.

=FV(rate,nper,pmt,pv)

Here rate is 5% or 0.05

Nper is number of period or 30 years

Pmt is periodic investments or $15000

And pv or present value is $2,000,000

=FV(0.05,30,15000,2000000)

= $9,640,467.46

Thus, money accumulated in this 30 year period is $9,640,467.46. Ignore negative sign of excel as it cash flow signs are opposite. First payments are made to receive this amount. Thus, opposite signs.

Now, periodic payment needs to be calculated for receiving money in last 20 years from this accumulated sum.

We can use =PMT function of excel for this

=PMT(rate,nper,pv,fv)

Here, rate is 0.05

Nper is 20 years

Pv is $9,640,467.46

Fv is future value which is zero

=PMT(0.05,20,9640467.46)

= $773,576.05

Thus, $773,576 can be withdrawn each year for 20 years.

Correct option is d.

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