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Fernando invested money in a 3–yr CD (certificate of deposit) that returned the equivalent of 3.8% simple interest. He invested $1000 less in a 6–month CD that had a 2% simple interest return. If the total amount of interest from these investments was $424.00, determine how much was invested in each CD.

Respuesta :

calculista

Answer:

The amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was $2,600

Step-by-step explanation:

Let

x -----> the amount invested at 3–yr CD

x-$1,000 ----> the amount invested at 6–month CD

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

3–yr CD

[tex]t=3\ years\\P=x\\r=0.038[/tex]

substitute in the formula above

[tex]I1=x(0.038*3)[/tex]

[tex]I1=0.114x[/tex]

6–month CD

[tex]t=6/12=0.5\ years\\P=x-1,000\\r=0.02[/tex]

substitute in the formula above

[tex]I2=(1,000-x)(0.02*0.5)[/tex]

[tex]I2=10-0.01x[/tex]

Remember that

the total amount of interest from these investments was $424.00

so

[tex]I1+I2=424[/tex]

substitute and solve for x

[tex]0.114x+10+0.01x=424[/tex]

[tex]0.115x=414[/tex]

[tex]x=\$3,600[/tex]

[tex]x-\$1,000=\$2,600[/tex]

therefore

The amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was $2,600

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