Question

Sarah Wiggum would like to make a single investment and have ​$ 1.3 million at the time of her retirement in 30 years. She has found a mutual fund that will earn 3% annually. How much will Sarah have to invest​ today? If Sarah invests that amount and could earn a 15% annual​ return, how soon could she​ retire, assuming she is still going to retire when she has ​$ ​1.3 million?   Click on the table icon to view the PVIF table LOADING... To have ​$ million at​ retirement, the amount Sarah must invest today is ​$ nothing. ​(Round to the nearest​ cent.)

Answer 1

A) The amount to be invested today to get $1.3 million after 30 years at 3% return is given by-

Present value of investment =future value /(1+interest rate) ^time

1300000*(1/((1+3%)^30) )

=1300000*PVIF(30,3%)

=1300000*0.4119867

=535582. 71

B) Let the time at which 535582.71 can be invested for retirement be x

Therefore,

Present value of investment = future value /(1+interest rate) ^ time

535582.71=1300000 /(1+15%) ^x

535582.71 =1300000 pvif(x,15%)

PVIF( x, 15%)=535582.71 /1300000

PVIF(x, 15%)=0.4119867

1/(1+15%)^x=0.4119867

1/0.4119867=(1+15%)^x

x=6.344819 years

Sarah could retire in 6.344819 or 6.34 years as compared to 30 years

(note if pvif values are given then you can easily find x, otherwise x will be calculated as -

1/0.4119867=(1+15%)^x

2.4272628=1.15^x

Taking log both side

Log(2.4272628)=xlog 1.15

X=log(2.4272628)/log(1.15)

x=6.34 years approx)