2. Jackie, a 25 year old client, want to retire by age 65 with $1,500,000. How much would she have to invest annually, assuming a 6% rate of return?

Question

2.	Jackie, a 25 year old client, want to retire by age 65 with $1,500,000.  How much would she have to invest annually, assuming a 6% rate of return?

campbell_st · Answer

this is an application of a geometric series.... the series is created  from the annual investment being compounded 

a = 1.06 r = 1.06 and n = 40  P is the annual investment


$$s _{40} = 1500000$$

us the formula

$$s _{n} =P \times (a \times(r^n -1))/(r -1)$$

$$15000000 = P \times (10.6(1.06^40 -1))(1.06 -1)$$

$$P = (1500000 \times 0.06)/(1.06^40 -1)$$

the person needs to invest $ 9692.30

campbell_st · Answer

oops it should read

$$1.06^{40}$$

campbell_st · Answer

where ever you see

$$1.06^40$$