Question

Of the following investments, which would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.a. Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments).b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).d. Investment D pays $2,500 at the end of 10 years (just one payment).e. Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).

Answer 1

Answer:

The investment with the lowest Present Value is D= $936.86

Explanation:

Giving the following information:

Assume that the effective annual rate for all investments is the same and is greater than zero. We will assume an effective rate of 10%.

A) Investment A pays $250 at the end of every year for the next 10 years.

First, we need to find the final value.

FV= {A*[(1+i)^n-1]}/i

A= annual payment

FV= {250*[(1.10^10)-1]}/0.10= 3984.36

Now, we can find the present value.

PV= FV/(1+i)^n

PV= 3,984.36/1.10^10= $1,536.14

B) Investment B pays $125 at the end of every 6 months for the next 10 years.

FV= {125*[(1.05^20)-1]}/0.05= 4,133.24

PV= 4,133.24/(1.05^20)= 1,557.77

C) pays $125 at the beginning of every 6 months for the next 10 years

It is the same as B, but it generates interest for one more period.

PV= 1,557.77*1.05= 1,635.67

D) pays $2,500 at the end of 10 years

PV= 2500/1.10^10= $963.86

E) Investment E pays $250 at the beginning of every year for the next 10 years.

It is the same as A, but it generates interest for one more period.

PV= 1,536.14*1.10= $1,689.75