Question

You have 2 different savings accounts. For Account​ A, the simple interest earned after 9 months is ​$5.70. For Account​ B, the simple interest earned after 27 months is ​$32.40. If the interest rate is 3.8​% 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.

Answer 1

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 = $\frac{9}{12}$ years

Interest rate = 3.8%

Interest earned = $5.70

Account B:

Time = 27 months = $\frac{27}{12}$ 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.

$SI = \dfrac{P\times R\times T}{100}$

Putting the values for Account A and finding the value of Principal:

$5.70 = \dfrac{P_A \times 3.8\times 9}{100\times 12}\\\Rightarrow P_A = \dfrac{570\times 12}{3.8\times 9}\\\Rightarrow P_A=\ 200$

Now, Putting the values for Account B and finding the value of Principal:

$32.40 = \dfrac{P_B \times 2.4\times 27}{100\times 12}\\\Rightarrow P_B = \dfrac{3240\times 12}{2.4\times 27}\\\Rightarrow P_B=\ 600$

Interest earned in one month i.e. $\frac{1}{12}$ years:

Account A:

$SI_A = \dfrac{200\times 3.8\times 1}{100\times 12}\\\Rightarrow SI_A = \ 0.63$

$SI_B = \dfrac{600\times 2.4\times 1}{100\times 12}\\\Rightarrow SI_B = \ 1.2$

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.