MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer:The amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was $2,600Step-by-step explanation:Letx -----> the amount invested at 3–yr CDx-$1,000 ----> the amount invested at 6–month CDwe know thatThe 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 thatthe total amount of interest from these investments was $424.00so[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]thereforeThe amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was $2,600