# 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.