Solving Simple Interest Problems using Systems of Equations The simple interest I earned after one year on a deposit of principal P in an account earning interest at an annual rate r is given by
(Notice that this is the Basic Percent Equation with percent r, base P and amount I.)
The problems below involve investing money in two different accounts, each paying annual simple interest at a different rate. For each problem, write one equation in two variables expressing a relationship between the principals invested in the accounts, and another equation involving the interest earned. Solve the system of the two equations then use the solution to answer the question.
Example: A total of $8000 is deposited in two simple interest accounts. One one account, the annual simple interest rate is 5%, and on the second account, the annual simple interest rate is 6%. How much should be invested in each account so that the total annual interest earned is $450? Step 1: Use two variables to define two unknown quantities.
Let x represent the principal invested in the account paying 5% interest.
Let y represent the principal invested in the account paying 6% interest.
Step 2: Write an equation involving the principal invested in the two accounts. 8000
Step 3: Write an equation involving the interest earned from the two accounts. Since the interest earned from each account is given by the product of its interest rate and principal, we have
Step 4: Solve the system consisting of the equations from Steps 2 & 3.
Solution: (3000, 5000)
Step 5: Use the solution of the system to answer the question.
$3000 should be invested at 5% and $5000 should be invested at 6%.
Example: A sports foundation deposited a total of $24,000 into two simple interest accounts. The annual simple interest rate on one account is 7%. The annual simple interest rate on the second ...