Question

I have $ 10,000 USD. You can invest in the following options at any time:

Investment A: Every dollar invested now yields $ 0.08 one year from today and 1.25 three years from now.

Investment B: Every dollar invested now yields $ 0.15 one year from today and 1.10 two years from now.

Investment C: Every dollar invested now yields 1.40 three years from now.

Consider that we are at the beginning of year 1.

Cash that is not invested can be allocated to money market funds each year, yielding 4% interest per year.

A maximum of $ 5,000 USD can be placed on each investment at any point in time.

Come up with a model that will maximize my cash six years from now (that is, the amount of money I will have available at the beginning of year 7), solve it, and specify the maximum amount I could receive.

Answer 1

So First of All we need to Calculate Effective Rate of Return in Each Investments.

IN THE BEGINNING OF YEAR ONE.

Investment A

Investment A is having $0.08 Yields for 1 year which means $1 will become $1.08 at the end of Year One.

Also,in Investment A $1 will become $1.25 at the end of Year Three.

EFFECTIVE RATE = 8%(0.08/1*100) FOR ONE YEAR AND (0.25/1*100)/3 = 8.33% FOR THREE YEAR

Investment B

Investment B is having $0.15 for 1 Year which means $1 will become $1.15 at the end of year one.

Also, in Investment B $1 will become $1.10 at the end of year two.

EFFECTIVE RATE = 15%(0.15/1*100) FOR ONE YEAR AND (0.10/1*100)/3 = 3.33% FOR THREE YEAR

Investment C

Investment C $1 will become $1.40 at the end of Year 3.

EFFECTIVE RATE = (0.40/1*100)/3 = 13.33% FOR THREE YEAR

For three year purpose Effective Rate of Return is Highest in Investment C i.e. around 13.33% {(1.4-1)/1*100}/3 SImple

So $5,000 will bebecome $7,000(1.40*5,000) After three years.

and Another $5,000 in Investment A for three years will become $6,250(1.25*5,000) After three years.

Total Cash Inflow After 3 Years will be $13,250 (7,000+6,250).

After Three years $13,250 to be allocated to money market funds (Investment is only for three years So will allocate to money market funds) @ risk free rate of 4% every year.

Assuming Simple Interest

Cashflow of Interest per year for Next Three year( i.e. beginning of 7th Year) is...

$13,250*4*100 = $530

$530*3 = $1590

After 6 Years at the beginning of 7th Year Amount in Hand will be

$13250 + $1590 = $14,840 (approximately).

Will receive $14,840.