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Example 3.33 from Elementary Algebra, 3.3 Solve Mixture Applications
Solve Mixture Applications: example 3.33
Stacey has $20,000 to invest in two different bank accounts. One account pays interest at 3% per year and the other account pays interest at 5% per year. How much should she invest in each account if she wants to earn 4.5% interest per year on the total amount?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
We will fill in a chart to organize our information. We will use the simple interest formula to find the interest earned in the different accounts.
The interest on the mixed investment will come from adding the interest from the account earning 3% and the interest from the account earning 5% to get the total interest on the $20,000.
The amount invested is the principal for each account.
We enter the interest rate for each account.
We multiply the amount invested times the rate to get the interest.
Notice that the total amount invested, 20,000, is the sum of the amount invested at 3% and the amount invested at 5%. And the total interest, is the sum of the interest earned in the 3% account and the interest earned in the 5% account.As with the other mixture applications, the last column in the table gives us the equation to solve.
Write the equation from the interest earned.
Solve the equation.
amount invested at 3%Find the amount invested at 5%. Check. Stacey should invest $5,000 in the account that
earns 3% and $15,000 in the account that earns 5%.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Remy has $14,000 to invest in two mutual funds. One fund pays interest at 4% per year and the other fund pays interest at 7% per year. How much should she invest in each fund if she wants to earn 6.1% interest on the total amount?
How did it go?