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.