How much was invested into each account?

Question

Kristina invests a total of $11,000 in two accounts. The first account earned a rate of return of 14% (after a year). However, the second account suffered a 9% loss in the same time period. At the end of one year, the total amount of money gained was $-530.00. How much was invested into each account?

$ ___________was invested in the account that gained 14% and 

$ ____________was invested in the account that lost 9%.

Answer 1

The formula for simple interest is:

Interest = Amount · rate · time

The rates should be expressed as a decimal. In your case, we're talking one year, so time = 1 and the interest formula reduces to:

Interest = amount · rate

In your problem, we have two amounts and two rates, so:

Interest = amount1 · rate1 + amount2 · rate2

Now let Let x be the amount1 invested in the 14% (0.14) account. The amount2 invested in the -9% (-0.09) account is $11,000 - x. The interest is -$530.

Interest = amount1 · rate1 + amount2 · rate2

-$530 = x(0.14) + (11,000 - x)(-0.09)

Solve for x.