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Susan purchased municipal bonds yielding annually and certificates of deposit yielding 11% annually. If Susan's investments amounted to $22,730 and the annual income is $2355.97, how much money is invested in bonds and how much money is invested in certificates of deposit?

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abidemiokin

If the amount Susan purchased municipal bonds yielding annually and certificates of deposit yielding 11%, the money invested in bonds will be  $4,811

Amount invested in the certificate will be expressed as  $22,730 - $4,811

= $17,919

Correct question:

Correct question:Susan purchased municipal bonds yielding 8% annually and certificates of deposit yielding 11% annually. If Susan's investments amounted to $22,730 and the annual income is $2355.97, how much money is invested in bonds, and how much money is invested in certificates of deposit?

Let the amount invested in municipal bond be P₁

Let the amount invested in the certificate be P₂

If Susan's investments amounted to $22,730, then;

P₁ + P₂ = 22730 .......................1

Also, if the annual income on both investments is  $2355.97, hence;

I₁ + I₂ =  2355.97 ,.....................2

The formula for calculating the interest is expressed as:

[tex]I=\frac{PRT}{100}[/tex]

Hence the individual interest can be calculated as;

[tex]I_1=P_1R_1T\\I_2 = P_2R_2T[/tex]

From equation 2;

I₁ = 2355.97 - I₂

2355.97 - I₂ = P₁R₁T

I₂ = 2355.97 - P₁R₁T .................3

Similarly from equation 1;

P₂ = 22730 - P₁

I₂ = (22730 - P₁) R₂T .................4

Equating 3 and 4

2355.97 - P₁R₁T =  (22730 - P₁) R₂T

Since R₁ = 8 and R₂ = 11

2355.97 - 0.08P₁T =  (22730 - P₁) 0.11T

2355.97 - 8P₁T = 2,500.3T - 11P₁T

Since T = 1year, hence:

2355.97 - 0.08P₁ =2,500.3 - 0.11P₁

- 0.08P₁ + 0.11P₁ = 2,500.3 - 2355.97

0.03P₁ = 144.33

P₁ = 144.33/0.03

P₁ = $4,811

The amount of money invested in bonds will be  $4,811

Amount invested in certificate will be expressed as  $22,730 - $4,811

= $17,919

Learn more here: https://brainly.com/question/18456266

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