Question

Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.

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

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

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

d. Investment D pays $2,500 at the end of 10 years (just one payment).

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

Answer 1

Answer>

Future Value = PV * (1+r)^n

Where

PV = Present Value of the amount

r = rate of interest

n= number of periods

Since effective annual rate of interest is same for all investment, following criteria are used to differentiate between the future values:

1> the amount which is getting compounded for MORE number of periods will be higher than the amount which is being compounded for the lesser number of periods.

2> If everything else remains same, amount which is received earlier has a greater future value than the amount which is received later

Now, we will compare two options at a time -

Option A versus option B - as per rule 1, clearly the amounts received in option A are being compounded for greater number of periods than option B. Hence A > B

Option A versus Option C - as per rule 1, clearly the amounts received in option A are being compounded for greater number of periods than option C. Hence A > C

Option A versus Option D - as per rule 1 & rule 2, clearly the amounts received in option A are being compounded for greater number of periods than option D and are also being received earlier. Hence A > D

Option A versus Option E - as per rule 2, clearly the amounts received in option A are being received earlier than amounts in option E. Hence A > E

Therefore, the correct answer is option A