Question

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.

Answer 1

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

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

`I=P(rt)`

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

`t=3\ years\\P=x\\r=0.038`

substitute in the formula above

`I1=x(0.038*3)`

`I1=0.114x`

6–month CD

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

substitute in the formula above

`I2=(1,000-x)(0.02*0.5)`

`I2=10-0.01x`

Remember that

the total amount of interest from these investments was $424.00

so

`I1+I2=424`

substitute and solve for x

`0.114x+10+0.01x=424`

`0.115x=414`

`x=\$3,600`

`x-\$1,000=\$2,600`

therefore

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