Solve the compound interest formula for the interest rate r using the properties of rational exponents. then use the obtained formula to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $10,000 and was worth $14,373.53 after 11 years.

Josalynn

Josalynn

Answered question

2021-01-10

Solve the compound interest formula for the interest rate r using the properties of rational exponents. then use the obtained formula to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $10,000 and was worth $14,373.53 after 11 years.

Answer & Explanation

faldduE

faldduE

Skilled2021-01-11Added 109 answers

14,373.53=10,000(1+r2)2(11) 
14,373.53=10,000(1+r2)22 
14,373.5310000=(1+r2)22 
(1+r2)22=14,373.5310000 
(1+r2)22=1.437353 
In(1+r2)22=In(1.437353) 
22In(2+r2)=In(1.437353) 
In(2+r)=In(1.437353)22+In2 
(2+r)=eIn(1.437353)22+In2) 
r=eIn(1.437353)22+In2) 
r=0.03325 
r=3.325% 

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