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 D pays $2,500 at the end of 10 years (just one payment). b. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments). c. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments). d. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).

Answer 1

Answer:

The investment that will have the highest future value is option b.

Explanation:

First lets suposse the effective annual rate is 10%  

a. Future value= $2,500  

c. First you must obtain the net present value of all cash flows with the formula attached, for example:  

NVP= ($250/(1+10%)^1)+($250/(1+10%^2)+($250/(1+10%^3)... and so on until year 10  

With the excel formula "NPV" you can calculate the net present value specifying the interest rate, the cash flows.  

The NPV= $1,536.14  

And then you calculate the future value of this answer with this formula:  

VF=VP(1+i)^n  

VF= $1,536.14*(1+10%)^10  

VF=$3,984.36  

b. If payments are due at the beginning of every year means that at year 0 you start with $250. You must calculate the NPV in this way  

NPV= $250+($250/(1+10%)^1)+ )+($250/(1+10%^2)+($250/(1+10%^3)... and so on until year 10  

NPV= $1,786,14

And then you calculate the future value of this answer:

VF= $1,786,14*(1+10%)^10  

VF=$4,632.79

d. First, you must convert the annual interest rate into semi-annually interest

10% Annually effective is 4,88% Semi-anually effective

NPV=$125+($125/(1+4,88%)^1)+ )+($125/(1+4,88%^2)+($125/(1+4,88%^3)... and so on until period 20

NPV=$1,698.75

And then you calculate the future value of this answer:

VF= $1,698 *(1+10%)^10  

VF=$4,405.37

The investment that will have the highest future value is option b.