Question

Greg invested $11,000 in two accounts.

• The first account pays 5% interest per year.
• The second account pays 8% interest per year.
Greg earned a total of $752.50 in interest at the end of the first year.
How much did Greg invest in the 5% account?

A) 6750
B) 3415
C) 5500
D) $4250

Answer 1

D; $4,250

Explanation:

Here, we want to know the amount that was invested in the 5% account

We proceed as follows;

Let the amount invested in the 5% interest account be $a and the amount invested in the 8% interest account be $b

We have it that the total investment amount is $11,000

Mathematically, since total is 11,000; we can add a and b to give this

a + b = 11,000 •••••••••(i)

Now, let us work with the interests

Interest earned will be;

Percentage of interest * Amount invested

For the 5% interest account, the interest earned will be;

5/100 * a = 5a/100 = 0.05a

For the 8% interest account , the interest earned will be;

8/100 * b = 0.08b

By adding the interests on both account, we can get the total amount of interest earned

We can have this as;

0.05a + 0.08b = 752.50 •••••(ii)

From equation i above;

b = 11,000 - a

Substitute this into ii

0.05a + 0.08(11,000-a) = 752.5

0.05a+ 880 - 0.08a = 752.5

0.08a-0.05a = 880-752.5

0.03a = 127.5

a = 127.5/0.03

a = $4,250