Question

Using the time value of money Helen wants to take the next four years off work to travel around the world. She estimates her annual cash needs at $31,000 (if she needs more, she will work odd jobs). Helen believes she can invest her savings at 10% until she depletes her funds. Requirements 1. How much money does Helen need now to fund her travels?

Answer 1

Answer:Helen needs $143871 to fund her travels.

Step-by-step explanation:

This is a present value annuity as Helen wants to save money in order to withdraw $31000 per annum therefore that is the payment she will get per annum for four straight years for her holiday which will sustain her without working during holidays.

Given :

Payment that she will be withdrawing on her savings per annum for holidays $31000

R interest rate of the savings which is 10%

N the number of periods for her withdrawals which is 4 years  

Formula used is the present value annuity formula which is

Present value annuity= payment ((1-(1/ ((1+R) ^N)/R))*(1+R) ^N

                                        =$31000 ((1-(1/((1+0.1)^4)/0.1))*(1+0.1)^4

                                         =$143871

Therefore Helen must save $143871 at a 10% saving rate in order to withdraw $31000 per annual continuously for four years consecutively on holiday in order to fulfill her requirements of not working for the whole four years.  

We substitute with the given values in order to get how Helen will be able to save for the whole four years because we already know the payment that is going to be made each year to her for holiday is $31000 which will satisfy her needs.  so Helen needs $143871