Question

You invest some money at 2% and 1000 more than twice this amount at 4%. If the total annual interest was $240, how much did you invest at each percent?

Answer 1

$2000 at 2% and $5000 at 4%

Explanation:

Let's call the amount invested at 2% 'X', so the amount invested at 4% is 2X+1000.

Then, if the total annual interest is 240, we have that:

X * 2% + (2X+1000) * 4% = 240

0.02X + 0.08X + 40 = 240

0.1X = 200

X = 200/0.1

X = $2000

If X is $2000, the second value is 2X+1000 = $5000

So it was invested $2000 at 2% and $5000 at 4%.

Answer 2

Amount invested in;

2% rate x = $2000

4% rate (2x+1000) = $5000

Explanation:

Let x represent the amount invested in 2% rate;

The amount invested in 4% rate = 2x + 1000

Given;

Annual interest = $240

Annual interest for 2% rate;

0.02 × x = 0.02x

Annual interest for 4% rate;

0.04 × (2x+1000) = 0.08x + 40

Total annual interest is;

0.02x + 0.08x + 40 = 0.10x + 40

Equating to the given value;

0.10x + 40 = 240

0.10x = 240-40 = 200

x = 200÷0.10

x = $2000

And

2x +1000 = 2(2000) + 1000 = $5000

Amount invested in;

2% rate x = $2000

4% rate (2x+1000) = $5000