Question

​ (Present value)  Sarah Wiggum would like to make a single investment and have

​$1.6

million at the time of her retirement in

28

years. She has found a mutual fund that will earn

5

percent annually. How much will Sarah have to invest​ today? If Sarah earned an annual return of

17

​percent, how soon could she then​ retire?  

a.  If Sarah can earn

5

percent annually for the next

28

​years, the amount of money she will have to invest today is

​$nothing.

​(Round to the nearest​ cent.)

Answer 1

a.Present value=1,600,000*Present value of discounting factor(rate%,time period)

=1,600,000/1.05^28

=1,600,000*0.255093637

=$408149.82(Approx)

b.We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

1,600,000=408149.82*(1.17)^n

(1,600,000/408149.82)=(1.17)^n

Taking log on both sides;

log (1,600,000/408149.82)=n*log 1.17

n=log (1,600,000/408149.82)/log 1.17

=8.70 years(Approx)