Question

Vien invested $880, part at 9% per annum and the rest at 12% per annum. After one year, the total interest earned was $79.50. How much did he invest at each year?

A. $400 at 9%, $480 at 12%
B. $320 at 9%, $560 at 12%
C. $440 at 9%, $440 at 12%
D. $600 at 9%, $280 at 12%

Answer 1

Vien invested $400 at 9% and $480 at 12% per annum. By setting up a system of equations with the total investment and the total interest, and solving it, we find the amounts invested at each interest rate.

Step-by-step explanation:

To determine how much Vien invested at each interest rate, we need to set up a system of equations based on the total amount invested and the total interest earned. Let's use two variables: x for the amount invested at 9% and y for the amount invested at 12%. We have two key pieces of information to help us:

• The total amount invested is $880.
• The total interest from both investments is $79.50 after one year.

We can express these as two equations:

1. x + y = $880
2. 0.09x + 0.12y = $79.50

Using these equations, we can solve for x and y by substitution or elimination method. Substituting the value of x from the first equation into the second one gives us an equation with only one variable, y, which we can solve. Once we find y, we go back to the first equation to find x. The correct amounts that Vien invested are $400 at 9% and $480 at 12%, which corresponds to choice A.