Question

Which of the following investments would have the highest future value at the end of 10 years? Which has the highest present value today? Rank the choices below from highest to lowest present value. Assume that the effective annual interest rate for all investments is the same and is greater than zero.

1. Investment A pays $250,000 at the beginning of every year for the next 10 years (a total of 10 payments).

2. Investment B pays $125,000 at the end of every 6-month period for the next 10 years (a total of 20 payments).

3. Investment C pays $125,000 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).

4. Investment D pays $2.5 million at the end of 10 years (just one payment).

5. Investment E pays $250,000 at the end of every year for the next 10 years (a total of 10 payments).

Answer 1

PV of annuity=A*[1-(1+r)^-n]/r ; FV of annuity=A*[(1+r)^n-1]/r

PV of annuity due=A*(1+r)[1-(1+r)^-n]/r ; FV of annuity=A*(1+r)[(1+r)^n-1]/r

where A=annuity payment; r=interest rate; n=no of periods

lets assume an interest rate of 10%

Investment A:

PV=250000*(1+10%)*[1-(1+10%)^-10]/.1 =1689755.95

FV=250000*(1+10%)*[(1+10%)^10-1]/.1 =4382791.76

Investment B:

PV=125000*[1-(1+5%)^-20]/.05 =1557776.29

FV=125000*[(1+5%)^20-1]/.05 =4133244.26

Investment C:

PV=125000*(1+5%)*[1-(1+5%)^-20]/.05 =1635665.10

FV=125000*(1+5%)*[(1+5%)^20-1]/.05 =4339906.47

Investment D:

PV=2500000/(1+10%)^10=963858.22

FV=2500000

Investment E:

PV=250000*[1-(1+10%)^-10]/.1 =1536141.77

FV=250000*[(1+10%)^10-1]/.1 =3984356.15

From these calculations;

• Highest Present and Future value is given by Investment A
• Ranking(highest to lowest present value) ; Investment A>C>B>E>D