Question

Paul splits an investment of $20000 , a portion earning simple interest at a rate of 3.8 % per year and the rest earning at a rate of 8.1 % per year in such a way that the return on the total investment is 6.165 %. How much money was invested at each rate?

Answer 1

Answer:

$9,000 (amount invested at 3.8%)

$11,000 (amount invested at 8.1%)

Explanation:

Let us calculate the total interest earned by both investments

Interest earned= 0.06165* 20,000= $ 1,233

Let principal invested at 3.8% be X

Use formula Interest= principal* rate*time in years

Interest= X*0.038*1= 0.038X

Principal invested at 8.1% be (20,000-X)

So Interest = (20,000-X)*0.081*1= 1,620-0.081X

Total interest earned = Interest at 3.8% + Interest at 8.1%

1,233= 0.038X + 1,620 -0.081X

Rearranging

0.043X= 387

X= 387/0.043

X= $9,000 (amount invested at 3.8%)

Substitute in equation

Principal invested at 8.1%= 20,000-X

= 20,000- 9,000

= $11,000 (amount invested at 8.1%)