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Answer:
Principal in account A = $200
Principal in account B = $600
Account B earned more interest in the first month.
Step-by-step explanation:
Given two accounts:
Account A:
Time = 9 months = [tex]\frac{9}{12}[/tex] years
Interest rate = 3.8%
Interest earned = $5.70
Account B:
Time = 27 months = [tex]\frac{27}{12}[/tex] years
Interest rate = 2.4%
Interest earned = $32.40
To find:
Principal in each account.
Most interest earned in the first month?
Solution:
First of all, let us have a look at the formula for Simple Interest.
[tex]SI = \dfrac{P\times R\times T}{100}[/tex]
Putting the values for Account A and finding the value of Principal:
[tex]5.70 = \dfrac{P_A \times 3.8\times 9}{100\times 12}\\\Rightarrow P_A = \dfrac{570\times 12}{3.8\times 9}\\\Rightarrow P_A=\$200[/tex]
Now, Putting the values for Account B and finding the value of Principal:
[tex]32.40 = \dfrac{P_B \times 2.4\times 27}{100\times 12}\\\Rightarrow P_B = \dfrac{3240\times 12}{2.4\times 27}\\\Rightarrow P_B=\$600[/tex]
Interest earned in one month i.e. [tex]\frac{1}{12}[/tex] years:
Account A:
[tex]SI_A = \dfrac{200\times 3.8\times 1}{100\times 12}\\\Rightarrow SI_A = \$0.63[/tex]
[tex]SI_B = \dfrac{600\times 2.4\times 1}{100\times 12}\\\Rightarrow SI_B = \$1.2[/tex]
Account B earned more interest in the first month.
Therefore, the answers are:
Principal in account A = $200
Principal in account B = $600
Account B earned more interest in the first month.