Lesson Typical investment problems
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<H2>Typical investment problems</H2> <H3>Problem 1</H3>Robert invested $10000 in two different accounts, one gives the annual interest of 6% and the other of 9%. How much did he invest in the lower account to get a yearly earning of $810? <B>Solution</B>Solution <pre> Let x = amount invested at 9%, in dollars. Then the amount at 6% is the rest (10000-x) dollars. The interest from the 9% amount is 0.09*x dollars. The interest from the 6% amount is 0.06*(10000-x) dollars. Your equation is interest + interest = total interest, or 0.09*x + 0.06*(10000-x) = 810 dollars. From the equation, express x and calculate the answer x = {{{(810 - 0.06*10000)/(0.09-0.06)}}} = 7000. <U>Answer</U>. The amount at 9% is $7000; the rest $10000-$7000 = $3000 is the amount at 6%. <U>Check</U>. 0.06*3000 + 0.09*7000 = 810 dollars. ! Correct ! </pre> <H3>Problem 2</H3>Monica invests a total of $22,500 in two accounts paying 8% and 6% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $1,420.00 <B>Solution</B> <pre> Let x be the amount invested at 8%, in dollars. Then the amount invested at 6% is (22500-x) dollars. The annual interest produced by the 8% account is 0.08x dollars. The annual interest produced by the 6% account is 0.06*(22500-x) dollars. The total annual interest is the sum 0.08x + 0.06*(22500-x) dollars. Write an equation for the total annual interest 0.08x + 0.06*(22500-x) = 1420 dollars. Simplify this equation and find x 0.08x + 0.06*22500 - 0.06x = 1420 0.08x - 0.06x = 1420 - 0.06*22500 0.02x = 70 x = 70/0.02 x = 3500. <U>ANSWER</U>. $3500 was invested at 8% and the rest 22500-3500 = 19000 dollars was invested at 6%. <U>CHECK</U>. 0.08*3500 + 0.06*19000 = 1420 dollars, total annual interest. ! correct ! </pre> My other lessons on solving single linear equations and word problems in one unknown are - <A HREF=https://www.algebra.com/algebra/homework/equations/How-to-solve-a-linear-equation.lesson>HOW TO solve a linear equation</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Using-linear-equations-to-solve-word-problems.lesson>Simple word problems to solve using a single linear equation</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/More-complicated-word-problems-to-solve-using-single-linear-equation.lesson>More complicated word problems to solve using a single linear equation</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/06-Typical-word-problems-from-the-archive-to-solve-by-reduction-to-single-linear-equation.lesson>Typical word problems to solve using a single linear equation</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Typical-problems-on-selling-and-buying-items.lesson>Typical problems on buying and selling items</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Advanced-word-problems-to-solve-by-reduction-to-single-linear-equation.lesson>Advanced word problems to solve using a single linear equation</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/HOW-TO-algebreze-and-solve-these-problems-using-one-eqn-in-one-unknown.lesson>HOW TO algebraize and solve these problems using one equation in one unknown</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Challenging-word-problems-to-solve-using-a-single-linear-equation.lesson>Challenging word problems to solve using a single linear equation</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Selected-word-problems-to-solve-by-reducing-to-single-linear-equation.lesson>Selected word problems to solve by reducing to single linear equation</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Solving-some-business-related-problems.lesson>Solving some business-related problems</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/HOW-TO-solve-these-simple-word-problems-MENTALLY-without-using-equations.lesson>HOW TO solve these simple word problems MENTALLY without using equations</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Time-equation-to-solve-some-Travel-and-Distance-problems.lesson>Using time equation to solve some Travel and Distance problems</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Using-price-equation-to-solve-some-business-related-problems.lesson>Using price equation to solve some business related problems</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Solving-simple-and-simplest-problems-by-the-backward-method.lesson>Solving problems by the backward method</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Solving-problems-on-the-remaining-amount.lesson>Solving more complicated problems by the backward method</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Solving-entertainment-problems-on-shortage-money.lesson>Solving entertainment problems on shortage of money</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/OVERVIEW-of-lessons-on-solving-linear-equations-and-word-problems-in-one-unknown.lesson>OVERVIEW of lessons on solving linear equations and word problems in one unknown</A> in this site.
