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?
2. After speaking with a number of banks, Helen learns she will only be able to invest her funds at 6%. How much does she need now to fund her travels?

Short answer

1. Present value of Amount Withdrawn = $98,265.66
2. Present value of Amount Withdrawn = $107,418.48

Step-by-step solution

Meaning of Capital Investment

A sum of money utilized to help an enterprise accomplish its objectives or acquire long-term assets is alluded to as a capital investment.

Calculating money does Helen need now to fund her travels

The present value of the amount withdrawn in future years, assuming a 10% return on investment, is calculated as follows:

Statement showing present value @10%
Year	Withdrawal	PV @10%	Present value
1	$31,000	0.90909	$28,181.79
2	$31,000	0.82645	$25,619.95
3	$31,000	0.75131	$23,290.61
4	$31,000	0.68301	$21,173.31
Present value of Amount Withdrawn			$98,265.66

The above calculations show that putting $98,265.66 into savings at a rate of 10% will cover Helen's annual cash outlay of $31,000 for four years of travel around the world.

Money needed by Helen to fund her travel.

The present value of the amount withdrawn in future years, assuming a 6% return on investment, is calculated as follows:

Statement showing present value @6%
Year	Withdrawal	PV @6%	Present value
1	$31,000	0.94340	$29,245.4
2	$31,000	0.89000	$27,590
3	$31,000	0.83962	$26,028.22
4	$31,000	0.79206	$24,553.86
Present value of Amount Withdrawn			$107,417.48

The amount invested today that will withdraw in the future is calculated by computing the present values of the amount to be withdrawn in future years discounted at the savings rate of interest.