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