Question

Santiago receives $251 Per year and simple interest from three investments. Part is invested at 2% part at 3% and part at 4%. There is $500 more invested at 3% then at 2%. The amount invested at 4% is six times the amount invested at 3%. Find the amount invested at each rate.

Answer 1

2% : $400

3% : $900

4% : $5400

Explanation:

Given that :

Total interest received = 251

Let investment at 2% = x

At 3% = 500 + x

At 4% = 6(500 + x) = 3000 + 6x

Simple interest :

Principal * rate * time

At 2%:

Simple interest = 0.02x

At 3%:

Simple interest = 0.03 * (500 + x) = 15 + 0.03x

At 4%:

Simple interest = 0.04 * (3000 + 6x) = 120 + 0.24x

0.02x + 15 + 0.03x + 120 + 0.24x = 251

0.29x + 135 = 251

0.29x = 116

x = 116 / 0.29

x = 400

Amount invested at 2% = x = $400

Amount invested at 3% = $500 + x = 500 + 400 = 900

Amount invested at 4% = 3000 + 6x = $3000 + 6(400) = $3000 + $2400 = $5400