Question

Dixon Shuttleworth has been offered the choice of three retirement-planning investments. The first investment offers a 5 percent return for the first 5 years, a 10 percent return for the next 5 years, and a 20 percent return thereafter. The second investment offers 10 percent for the first 10 years and 15 percent thereafter. The third investment offers a constant 12 percent rate of return. Determine, for each of the given number of years, which of these investments is the best for Dixon if he plans to make one payment today into one of these funds and plans to retire in the following number of years.

a. 15 years
b. 20 years
c. 30 years

Answer 1

a. If you plan to retire in 15 years, you should accept the third investment plan.

b. If you plan to retire in 20 years, you should accept the first investment plan.

c. If you plan to retire in 30 years, you should accept the first investment plan.

Step-by-step explanation:

Assuming that Dixon invests $100 today:

1) value of first investment offer:

15 years

$100 x 1.05⁵ = $127.63

$127.63 x 1.1⁵ = $205.55

$205.55 x 1.2⁵ = $511.47

20 years

$100 x 1.05⁵ = $127.63

$127.63 x 1.1⁵ = $205.55

$205.55 x 1.2¹⁰ = $1,272.69

30 years

$100 x 1.05⁵ = $127.63

$127.63 x 1.1⁵ = $205.55

$205.55 x 1.2²⁰ = $7,880.16

2) value of second investment offer:

15 years

$100 x 1.1¹⁰ = $259.37

$259.37 x 1.15⁵ = $521.69

20 years

$100 x 1.1¹⁰ = $259.37

$259.37 x 1.15¹⁰ = $1,049.31

30 years

$100 x 1.1¹⁰ = $259.37

$259.37 x 1.15²⁰ = $4,245.06

3) value of third investment offer:

15 years

$100 x 1.12¹⁵ = $547.36

20 years

$100 x 1.12²⁰ = $964.63

30 years

$100 x 1.12³⁰ = $2,995.99