# Determine the present value if $15,000 is to be received at the end of eight years and the...

## Question:

Determine the present value if $15,000 is to be received at the end of eight years and the discount rates is 9 percent. How would your answer change if you had to wait six years to receive $15,000?

## Present value:

Present value is a part of the time value of money concept. This concept is used to calculate the power of money received today compared with the power of money received in the future.

## Answer and Explanation:

Let us calculate present value with the help of a formula:

{eq}\boldsymbol{PV} = \boldsymbol{\frac{FV}{(1+r)^n}} {/eq}

where,

- PV = Present value = to be calculated
- FV = Future value = $15,000
- r = rate of return = 9% i.e 0.09
- n = number of periods = 8 years

{eq}\boldsymbol{PV} = \boldsymbol{\frac{15000}{(1+0.09)^8}} {/eq}

{eq}\boldsymbol{PV} = \boldsymbol\$7,528 {/eq}

Let us see how the answer change if we have to wait for 6 years instead of 8 years:

{eq}\boldsymbol{PV} = \boldsymbol{\frac{FV}{(1+r)^n}} {/eq}

where,

- PV = Present value = to be calculated
- FV = Future value = $15,000
- r = rate of return = 9% i.e 0.09
- n = number of periods = 6 years

{eq}\boldsymbol{PV} = \boldsymbol{\frac{15000}{(1+0.09)^6}} {/eq}

{eq}\boldsymbol{PV} = \boldsymbol\$8,944 {/eq}

**If you had to wait for 6 years instead of 8 years the present value increases since the time period has been reduced. Thus, you have to invest more to receive the same amount in short span of time.**

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from Introduction to Business: Homework Help Resource

Chapter 24 / Lesson 15