Question

a)     A woman who has won a prize is offered a lump sum of 100000 to invest now or 55000 to invest at the end of this year .If all investments are assumed to earn 7% per annum which should she choose if she wants to withdraw the money after

i)                  4 years

2 years             

Answer 1

A) If she invests the 100000 as a lump sum, after 4 years, she'd be able to withdraw

$FV=100000(1+0.07)^4$

$FV_4=131079.60$

If she invests 55000 at the end of the year, after 4 years, she'd be able to withdraw

$FV=\frac{55000[(1+0.07)^4-1]}{0.07}$

$FV_4=244196.87$

She'd choose to invest the 55000 at the end of the year as it pays more after 4 years.

B) if she chooses the 100000 plan to withdraw after 2 years:

$FV=100000(1+0.07)^2$

$FV_2=114490$

If she chooses the 55000 plan to withdraw after 2 years:

$FV=\frac{55000[(1+0.07)^2-1]}{0.07}$

$FV_2=113850$

She'd choose the 100000 plan to withdraw because it pays more after 2 years.