Here is the question Attempts Score 1 30 You know that youll

Here is the question

Attempts: Score: /1 30. You know that you\'ll need to purchase a new piece of equipment for your recording studio... You know that you\'ll need to purchase a new piece of equipment for your recording studio in 4 years, with an anticipated cost of $55,000. You have found a stock that has averaged an 11% rate of return and you want to make a one-time deposit. How much do you need to invest today in order to have the $55,000 at the end of year 4? $32,639.82 $39,462.98 $36,230.20 $170,634.51

Solution

The Correct answer is $36,230.20

The equipment will be purchased in 4 years and it will cost $55,000. Since the amount has to be spent at a future date to acquire the equipment, $55,000 is the Future Value.

We will be required to find out as to what amount that needs to be invested today so that at the end of 4th year we will be left with $55,000. This is known as Present Value.

Future Value = Present Value * (1 + i)ⁿ

Where, Future Value = $55,000

i = Required rate of return

i = 11%

n = number of years

n = 4

Therefore

Future Value = Present Value * (1 + i)ⁿ

$55,000 = Present Value * (1 + 11%)⁴

$55,000 = Present Value * (1 + 0.11)⁴

$55,000 = Present Value * (1.11)⁴

$55,000 = Present Value * 1.51807041

Present Value = $55,000 / 1.51807041

Present Value = $36,230.20 (rounded two decimal places)