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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
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