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 ea

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?

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3 weeks 2022-01-01T15:49:18+00:00 2 Answers 0 views 0

Amount invested in;

2% rate x = \$2000

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

Step-by-step 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

\$2000 at 2% and \$5000 at 4%

Step-by-step 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%.