Question

Which of the following investments would you prefer?

Multiple Choice

• an investment earning 4 percent for 30 years

• an investment earning 5 percent for 20 years

• an investment earning 6 percent for 10 years

• an investment earning 3 percent for 40 years

Answer 1

Option (c) is the answer

Here we will calculate the present values of all the investments and check the investment with highest present value. We will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value = Suppose future value is $1, PV = Present value, r = rate of interest , n= time period

Investment earning 4% for 30 years:

FV = Future value = Suppose future value is $1, PV = Present value, r = rate of interest =4% , n= time period =30

now, putting these values in the above equation, we get,

PV = $1 / (1 + 4%)30

PV = $1 / (1 + 0.04)30

PV = $1 / (1.04)30

PV = $1 / 3.24339751003

PV = $0.3083

So, present value is $0.3083.

Investment earning 5% for 20 years:

FV = Future value = Suppose future value is $1, PV = Present value, r = rate of interest =5% , n= time period = 20

now, putting these values in the above equation, we get,

PV = $1 / (1 + 5%)20

PV = $1 / (1 + 0.05)20

PV = $1 / (1.05)20

PV = $1 / 2.65329770514

PV = $0.37689

So, present value is $0.37689.

Investment earning 6% for 10 years:

FV = Future value = Suppose future value is $1, PV = Present value, r = rate of interest =6% , n= time period =10

now, putting these values in the above equation, we get,

PV = $1 / (1 + 6%)10

PV = $1 / (1 + 0.06)10

PV = $1 / (1.06)10

PV = $1 / 1.79084769654

PV = $0.5584

So, present value is $0.5584.

Investment earning 3% for 40 years:

FV = Future value = Suppose future value is $1, PV = Present value, r = rate of interest =3% , n= time period =40

now, putting these values in the above equation, we get,

PV = $1 / (1 + 3%)40

PV = $1 / (1 + 0.03)40

PV = $1 / (1.03)40

PV = $1 / 3.262937792

PV = $0.30655

So, present value is $0.30655.

Since the investment of 6% for 10 years has highest present value of $0.5584, so it should be preferred.