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  You have 2 different savings accounts. For Account​ A, the simple interest earned after 15 months is ​$9.25. For Account​ B, the simple interest earned after 27 months is ​$21.60. If the interest rate is 3.7​% for Account A and 2.4​% for Account​ B, how much is the principal in each​ account? Which account earned you the most interest the first​ month? Explain your answer

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Answer:

Principal in Account A: $16.67

Principal in Account B: $33.33

Account B earned the most interest in the first month.

Step-by-step explanation:

Use the simple interest formula: [tex]I = Prt[/tex]

"I" represents total interest earned

"P" is principal, the starting amount

"r" is the rate of interest in decimal form. Find this by dividing percentage by 100.

"t" is the time where interest was earned

Substitute all the information you know into the equation. Then isolate "P" to find the principal. Next, use the formula to calculate the interest for 1 month.

Account A

t = 15

I = 9.25

r = 3.7%   ==> Convert to decimal: 3.7/100 = 0.037

Find principal:

I = Prt

9.25 = P(0.037)(15)

9.25 = 0.555P    <=Divide both sides by 0.555

P = 16.67

First month interest:

I = Prt

I = 16.67(0.037)(1)

I = 0.62

Account B

t = 27

I = 21.60

r = 2.4%   ==> Convert to decimal: 2.4/100 = 0.024

Find principal:

I = Prt

21.60 = P(0.024)(27)

21.60 = 0.648P    <= Divide both sides by 0.648

P = 33.33

First month interest:

I = Prt

I = 33.33(0.024)(1)

I = 0.80

The first month interest in Account B was more than in Account A.

0.80 > 0.62

Therefore, the principal in Account A is $16.67. The principal in Account B is $33.33. Account B earned the most interest in the first month.