Question

4.3 Calculating Present Values For each of the following, compute the present value:

Present Value                   Years                    Interest Rate                     Future Value

6                            7%                                       $ 13,827

11                         15                                        $ 43,852

19                         11                                        $725,380

29                         18                                        $590,710

Answer 1

Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value, PV = Present value r = rate of interest, n= time period

(a) FV = Future value = $13827, r = rate of interest = 7%, n= time period = 6

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

PV = $13827 / (1 + 7%)⁶

PV = $13827 / (1 + 0.07)⁶

PV = $13827 / (1.07)⁶

PV = $13827 / 1.50073035185

PV = $9213.51

(b) FV = Future value = $43852, r = rate of interest = 15%, n= time period = 11

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

PV = $43852 / (1 + 15%)¹¹

PV = $43852 / (1 + 0.15)¹¹

PV = $43852 / (1.15)¹¹

PV = $43852 / 4.65239139606

PV = $9425.69

(c) FV = Future value = $725380, r = rate of interest = 11%, n= time period = 19

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

PV = $725380 / (1 + 11%)¹⁹

PV = $725380 / (1 + 0.11)¹⁹

PV = $725380 / (1.11)¹⁹

PV = $725380 / 7.26334372624

PV = $99868.60

(d) FV = Future value = $590710, r = rate of interest = 18%, n= time period = 29

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

PV = $590710 / (1 + 18%)²⁹

PV = $590710 / (1 + 0.18)²⁹

PV = $590710 / (1.18)²⁹

PV = $590710 / 121.500541049

PV = $4861.79