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Your rich uncle has just given you a high school graduation present of $1 million. The present,...

Question:

Your rich uncle has just given you a high school graduation present of {eq}$1 {/eq} million. The present, however, is in the form of a {eq}40 {/eq} year bond with an annual interest rate of {eq}9 {/eq}% compounded annually. The bond says that it will be worth {eq}$1 {/eq} million in {eq}40 {/eq} years. What is this gift worth at the present time?

Present Value

This problem is based on the application of the concept of estimating the present value. It is a formula that calculates the present-day value of an amount that is received at a future date. So, we are going to use the present value formula to figure out the solution.

Answer and Explanation:


The present value of the gift can be obtained by using the formula for the present value and that is given by,

{eq}\displaystyle \text{Present Value}=P\times \left ( \frac{1}{(1+r)^n} \right ) {/eq}

Where,

{eq}\displaystyle P=\text{Payment} {/eq}

{eq}\displaystyle r=\text{rate of interest} {/eq}

{eq}\displaystyle n=\text{number of periods}=40 {/eq}

So,

{eq}\displaystyle \text{Present Value}=1,000,000\times \left ( \frac{1}{(1+0.09)^{40}} \right ) {/eq}

{eq}\displaystyle \text{Present Value}=1,000,000\times \left ( \frac{1}{(1.09)^{40}} \right ) {/eq}

{eq}\displaystyle \text{Present Value}=1,000,000\times \left ( \frac{1}{31.4094} \right ) {/eq}

The worth of gift in the present time is:

{eq}\displaystyle \boxed{\displaystyle \text{Present Value}=\$31,837.58} {/eq}


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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