Question

An accountant has money in three accounts that pay 10%, 11%, and 12% in annual interest. He has twice as much invested at 10% as he does at 11% and three times as much invested at 12% as he does at 11%. If the total interest from the three accounts is $670 for the year, how much is invested at each rate? (Hint: Let x = the amount invested at 11%.)

a) Amount invested at 10% $
b) Amount invested at 11% $
c) Amount invested at 12% $

Answer 1

To determine the amounts invested at each interest rate, assign variables and set up an equation using the given information. Solve the equation to find the values of the variables.

Step-by-step explanation:

Let's assign variables to represent the amounts invested at each rate. Let x be the amount invested at 11%. Since the accountant has twice as much invested at 10% as he does at 11%, the amount invested at 10% is 2x. Similarly, he has three times as much invested at 12% as he does at 11%, so the amount invested at 12% is 3x.

We know that the total interest from the three accounts is $670 for the year. The interest earned at 10% is 10% of the amount invested at 10%, which is 0.1 * 2x = 0.2x. The interest earned at 11% is 11% of the amount invested at 11%, which is 0.11 * x. The interest earned at 12% is 12% of the amount invested at 12%, which is 0.12 * 3x = 0.36x.

Therefore, we can set up the equation: 0.2x + 0.11x + 0.36x = 670. Solving this equation will give us the values of x, 2x, and 3x, which represent the amounts invested at each rate.