Question

Give an example of a retirement planning problem whose solution involves calculating the present value of multiple cash flows. Give another example whose solution involves calculating the future value of multiple cash flows.

Answer 1

First calculating the future value of the cash flows:

Cash flow schedule:

                   0            1            2           3           4               5

                            1000       1000     1000     1000      1000

To calculate the future value of cash flows for the next five years & you invest each payment at 5% interest.

Years       cash flows       future value

0

1              1000                 =1000*(1.05)^4 = $1215.51

2              1000                 =1000*(1.05)^3 = $1157.63

3              1000                 = 1000*(1.05)^2 = 1102.50

4              1000                 =1000*(1.05)^1   = 1050

5             1000                 =1000*(1.05)^0    = 1000

                                                                         $5525.64

This can also be calculated using the formula:

FV ordinary annuity = c*(1+i)^n – 1/i

= 1000*(1+0.05)^5 – 1/0.05

$5525.63

For calculating the present value, the formula is:

PV ordinary annuity = c*(1- (1+i)^-n/i

= 1000*(1-(1+0.05)^-5/0.05

= $4329.48