The Lexington Property Development company has a $10,000 note receivable from a customer due in...

Question:

The Lexington Property Development company has a $10,000 note receivable from a customer due in three years. How much is the note worth today if the interest is:

a. 9%

b. 12% compounded monthly

c. 8% compounded quarterly

d. 18% compounded monthly

e. 7% compounded continuously?

Present value:

Present value refers to the estimated equivalent present amount of the sum of the money in the future based on its discounted interest rate. It is one component of the concept of the time value of money, which indicates that the present sum of money has greater value in real terms compared to its identical sum in the future.

Answer and Explanation:

Formula on calculating the present value of the receivable:

{eq}PV=FV*(1+\frac{r}{m})^{-nm}\\ whereas:\\ FV=future~value\\ r=interest~rate\\ n=number~of~periods\\ m=number~of~payments\\ {/eq}


Question (a)

{eq}\begin{align*} PV&=10000.00*(1+\frac{.09}{1})^{-3*1}\\ &=10000.00*(1.09)^{-3}\\ &=10000.00*0.77218\\ &=7721.83 \end{align*} {/eq}

The present value of the $10,000 note receivable in three years at 9% interest rate is $7721.83


Question (b)

{eq}\begin{align*} PV&=10000.00*(1+\frac{.12}{12})^{-3*12}\\ &=10000.00*(1.01)^{-36}\\ &=10000.00*0.69892\\ &=6989.25 \end{align*} {/eq}

The present value of the $10,000 note receivable in three years at 12% interest rate compounded monthly is $6989.25


Question (c)

{eq}\begin{align*} PV&=10000.00*(1+\frac{.08}{4})^{-3*4}\\ &=10000.00*(1.02)^{-12}\\ &=10000.00*0.78849\\ &=7884.93 \end{align*} {/eq}

The present value of the $10,000 note receivable in three years at 8% interest rate compounded quarterly is $7884.93


Question (d)

{eq}\begin{align*} PV&=10000.00*(1+\frac{.18}{12})^{-3*12}\\ &=10000.00*(1.015)^{-36}\\ &=10000.00*0.58509\\ &=5850.90 \end{align*} {/eq}

The present value of the $10,000 note receivable in three years at 18% interest rate compounded monthly is $7884.93


Question (e)

{eq}PV=FVe^{-rn}\\ whereas:\\ FV=future~value\\ e=2.71828\\ r=interest~rate\\ n=number~of~periods\\ {/eq}


{eq}\begin{align*} PV&=10000.00*2.718282^{(.07*3)}\\ &=10000.00*2.718282^{-.21}\\ &=10000.00*.8106\\ &=8105.84 \end{align*} {/eq}

The present value of the $10,000 note receivable in three years at 7% interest rate compounded continuously is $4317.11


Learn more about this topic:

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How to Calculate Present Value of an Investment: Formula & Examples

from Introduction to Business: Homework Help Resource

Chapter 24 / Lesson 15
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