Question

Measured it today's dollars, how much better is it to receive $2,032 in 4 years than to receive $5,941 in 15 years, if the rate of return is 8.4% per year?

Answer 1

Here, we will calculate the present value of both the options.

Present value of $2032 in 4 years:

Here we will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value = $2032, PV = Present value, r = rate of interest = 8.4%, n= time period = 4

Now,putting the values in the above equation, we get,

PV = $2032 / (1 + 8.4%)4

PV = $2032 / (1 + 0.084)4

PV = $2032 / (1.084)4

PV = $2032 / 1.38075660314

PV = $1471.66

So, present value is $1471.66

Present value of $5941 in 15 years:

Here we will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value = $5941, PV = Present value, r = rate of interest = 8.4%, n= time period = 15

Now,putting the values in the above equation, we get,

PV = $5941 / (1 + 8.4%)15

PV = $5941 / (1 + 0.084)15

PV = $5941 / (1.084)15

PV = $5941 / 3.35304385008

PV = $1771.82

So, present value is $1771.82

Present value of second option i.e. $5941 in 15 years is greater than the present value of receiving $2032 by:

$1771.82 - $1471.66 = $300.16.