Question

Ms. Rowling has a goal is to be able to withdraw $10,700 for each of the next eight years beginning one year from today and also to withdraw $57,000 ten years from today. The return on an investment fund is expected to be 5% per annum. The amount that Ms. Rowling need to invest in the fund today is closest to:

Answer 1

Ms. Rowling has a goal to withdraw 10700 each of the next eight years

Return on investment is 5%per annum

So Ms Rowling need to invest today is

P=PMT*[{1-1/(1+r)n}/r]*(1+r)

where, P=Present value

PMT=Amount of each annuity=10700

r=Rate of return=0.05

n=Numer of period=8

so, according to above formula,

P= 10700*[{1-1/(1+0.05)8}/0.05]*(1+0.05)

  = 10700*[{1-1/1.48}/0.05]*1.05

=10700*[{1-.068}/0.05]*1.05

=10700*[0.32/0.05]*1.05

=10700*6.4*1.05

=71904

if Ms. Rowling has a goal to withdraw 57000 each of the next ten years

Return on investment is 5%per annum

So Ms Rowling need to invest today is

P=PMT*[{1-1/(1+r)n}/r]*(1+r)

where, P=Present value

PMT=Amount of each annuity=57000

r=Rate of return=0.05

n=Numer of period=10

so, according to above formula,

P= 57000*[{1-1/(1+0.05)10}/0.05]*(1+0.05)

P=57000*[{1-1/(1.63)}/0.05]*(1+0.05)

P=57000*[{1-0.61}/0.05]*1.05

P=57000*[0.39/0.05]*1.05

P=57000*7.8*1.05

P=466830

So Ms Rowling has to invest a total of (71904+466830)=$538734