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.
