Q22E
Expert-verifiedUsing 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
A sum of money utilized to help an enterprise accomplish its objectives or acquire long-term assets is alluded to as a capital investment.
The present value of the amount withdrawn in future years, assuming a 10% return on investment, is calculated as follows: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Present value of Amount Withdrawn | $98,265.66 |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.
The present value of the amount withdrawn in future years, assuming a 6% return on investment, is calculated as follows: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Present value of Amount Withdrawn | $107,417.48 |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invested today that will withdraw in the future is calculated by computing the present values of the amount to be withdrawn in future years discounted at the savings rate of interest.
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