littlesammy33
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Two investments totaling $63,500 produce an anual income of $3250. One investment yields 4% per year, while the other yields 6% per year. How much is invested at each rate?

Respuesta :

frika

Answer:

$28,000 at 4% rate

$35,500 at 6% rate

Step-by-step explanation:

Let $x be the first amount of investment, then $(63,500-x) is the amount of the second investment.

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest

P = principal (initial amount of investment)

r = rate

t = time.

In your case,

[tex]I=\$3,250\\ \\r_1=0.04\\ \\r_2=0.06\\ \\t_1=t_2=1\\ \\P_1=\$x\\ \\P_2=\$(63,500-x)[/tex]

Hence

[tex]I_1=x\cdot 0.04\cdot 1\\ \\I_2=(63,500-x)\cdot 0.06\cdot 1\\ \\I=I_1+I_2[/tex]

So,

[tex]0.04x+0.06(63,500-x)=3,250\\ \\0.04x+3,810-0.06x=3,250\\ \\-0.02x=3,250-3,810\\ \\-0.02x=-560\\ \\2x=56,000\\ \\x=28,000\\ \\63,500-x=63,500-28,000=35,500[/tex]

francocanacari

$35,500 were invested at 6% and $28,000 were invested at 4%.

Calculus

Given that two investments totaling $63,500 produce an annual income of $3,250, and one investment yields 4% per year, while the other yields 6% per year, to determine how much is invested at each rate, the following calculation must be performed:

  • 63500 x 0.06 + 0 x 0.04 = 3810
  • 0 x 0.06 + 63500 x 0.04 = 2540
  • 43500 x 0.06 + 20000 x 0.04 = 3410
  • 20000 x 0.06 + 43500 x 0.04 = 2940
  • 33500 x 0.06 + 30000 x 0.04 = 3210
  • 35500 x 0.06 + 28000 x 0.04 = 3250

Therefore, $35,500 were invested at 6% and $28,000 were invested at 4%.

Learn more about calculus in brainly.com/question/24393912

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