13. Q13
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Similar Question 1
<p>Five years ago, money was invested at 7% per year, compounded annually. Today the investment is worth $441.28.</p><p>(a) How much money was originally invested?</p><p>(b) How much interest was earned?</p> Similar Question 2 <p>Sean invests some money in an account that earns a rate of interest compounded annually. The amounts of the investment at the end of the first three years are shown at the below?</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &year 1 & \$4240.00 \\ &year 2 & \$4494.40 \\ &year 3 & \$4764.06 \end{array} </code></p><p><strong>a)</strong> Determine the annual rate of compounded interest earned.</p><p><strong>b)</strong> How much did Sean invest?</p>
Similar Question 3
<p>Cal used the exponential function <code class='latex inline'>A(n) = 5000 \times 1.0075^{12n}</code> to represent the future value, <code class='latex inline'>A</code>, in dollars, of an investment. Determine the principal, the annual interest rate, and the compounding period. Explain your reasoning.</p>
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Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
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<p>In 6 years, money invested 7.5% per annum, compounded quarterly, will grow to $807.21.</p><p>(a) How much money was invested?</p><p>(b) How much interest will be earned in 6 years?</p> <p>Tracey would like to have$10000 in 4 years to use as a down payment for house. She is considering two investment options: </p><p><strong>Investment A</strong>: 6.6% annual interest, compounded semi-annually.</p><p><strong>Investment B</strong>: 6.2% annual interest, compounded monthly.</p> <ul> <li>(a) Compare the present values of the two options.</li> <li>(b) Which investment is the better choice for Tracey? Explain your reasoning.</li> </ul>
<p>Conrad buys a stereo. He pays $500 now and agrees to pay$2000 in three years.</p> <ul> <li>(a) If interest on the money is compounded quarterly at 16% per annum, determine the cash value of the stereo now.</li> <li>(b) How much money would Conrad save if he paid cash of the stereo when he bought it?</li> </ul>
<p>Four and a half years ago, some money was deposited into an account that paid an annual interest rate of 3.2%, compounded semi-annually. Today, the account has a value of $821.36. What was the amount of the original deposit? </p> <p>Five years ago, money was invested at 7% per year, compounded annually. Today the investment is worth$441.28.</p><p>(a) How much money was originally invested?</p><p>(b) How much interest was earned?</p>
<p>In 4 years, an investment will be worth $506.99. If interest is earned at a rte of 6% per year, compounded annually, what is the present value o this investment?</p> <p>Sean invests some money in an account that earns a rate of interest compounded annually. The amounts of the investment at the end of the first three years are shown at the below?</p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &year 1 & \$4240.00 \\ &year 2 & \$4494.40 \\ &year 3 & \$4764.06 \end{array} </code></p><p><strong>a)</strong> Determine the annual rate of compounded interest earned.</p><p><strong>b)</strong> How much did Sean invest?</p>
<p>Determine the present value of each <code class='latex inline'>n</code> future amount for the given conditions.</p><p> In 3 years, an investment earning 4.8% annual interest, compounded quarterly, will have a value of $1021.86.</p> <p>A loan is to be repaid in five years. Interest is accumulating on the loan at the rate of 8% per annum compounded quarterly. The payment required to retire the loan in five years is$ 6686.76. Find the present value of the loan.</p>
<p>Michael needs <code class='latex inline'>\displaystyle \$500 </code> two years from now. The amount to be invested, <code class='latex inline'>\displaystyle A </code>, at an interest rate <code class='latex inline'>\displaystyle i </code> is given by the relation <code class='latex inline'>\displaystyle A(i)=\frac{500}{(1+i)^{2}} </code>. Note that <code class='latex inline'>\displaystyle i </code> must be expressed as a decimal.</p><p>a) Determine the domain and range for</p><p>this relation.</p><p>b) Is this relation a function? Explain. c) How much money needs to be</p><p>invested at each interest rate?</p><p>i) <code class='latex inline'>\displaystyle 4 \% </code></p><p>ii) <code class='latex inline'>\displaystyle 8 \% </code></p><p>d) At what rate of interest would each</p><p>amount need to be invested?</p><p>i) <code class='latex inline'>\displaystyle \$ 350 </code></p><p>ii) <code class='latex inline'>\displaystyle \$400 </code></p> <p>Cal used the exponential function <code class='latex inline'>A(n) = 5000 \times 1.0075^{12n}</code> to represent the future value, <code class='latex inline'>A</code>, in dollars, of an investment. Determine the principal, the annual interest rate, and the compounding period. Explain your reasoning.</p> <p>The future value of a lan due to a financial institution in 10 years is$50 000. The financial institution is willing to sell the debt today discounted at 6% per year, compounded semi-annually. What is the value of the debt today?</p>
<p>Patricia receives a financial gift from her grandparents, which she invests at <code class='latex inline'>8\%</code> annual interest, compounded semi-annually. She is advised that the investment will be worth <code class='latex inline'>\\$ 3421.40</code> in <code class='latex inline'>4</code> years.</p><p>(a) What is the amount of the gift?</p><p>(b) How much interest will Patricia&#39;s investment earn?</p>
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