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Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest. What rate of interest did the certificate pay? Show all of your work.

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Answer:

Sylvia was paid 22% rate of interest.

Step-by-step explanation:

We are given that Sylvia bought a 6-month $1900 certificate of deposit.

Time of deposit = 6 months [tex]\frac{1}{2}[/tex] of a year.

Let us assume rate of interest = R% per year.

Formula of simple interest I = PRT, where P is the bond amount, R is the rate of interest per year and T is the time in years.

Plugging values I=209, P= 1900, R= R%  and T= [tex]\frac{1}{2}[/tex] in above formula, we get

209 = 1900×R×[tex]\frac{1}{2}[/tex]

On simplifying right side, we get

209=950R

Dividing both sides by 950, we get

[tex]\frac{209}{950} =\frac{950R}{950}[/tex]

R= 0.22

Converting 0.22 into % by multiplying by 100, we get 22%.

Therefore, Sylvia was paid 22% rate of interest.