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 $$I=P(rt)$$ 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 thatthe total amount of interest from these investments was$424.00so$$I1+I2=424$$substitute and solve for x$$0.114x+10+0.01x=424$$$$0.115x=414$$$$x=\3,600$$$$x-\1,000=\2,600$$thereforeThe amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was$2,600