Dana invests $10,000 into two accounts. One account earns 7% interest and the other earns 12% interest. After one year her total interest earned from the two accounts totals $965. How much did Dana invest in the 12% account? Type in your numerical answer only; do not type the $ symbol or any words or letters with your answer.

5300

Explanation:

Let;

amount in account 1 be denoted as x

amount in account 2 be denoted as y

Therefore;

x + y = $10,000 ... equation 1

Account 1 earns 7% interest,

7% of x = 0.07x

Account 2 earns 12% interest,

12% of y = 0.12y

Total interest earned after 1 year = $965

therefore;

0.07x + 0.12y = 965 ... equation 2

From equation 1,

x = 10000 - y ... equation 3

If we substitute equation 3 into equation 2, we have;

0.07 (10000 - y) + 0.12y = 965

700 - 0.07y + 0.12y = 965

0.12y - 0.07y = 965 - 700

0.05y = 265

y = 265 : 0.05

y = $5300

Therefore the amount Dana invested into the 12% account is $5300