Question

You have 2 different savings accounts. For Account​ A, the simple interest earned after 21 months is ​$13.65. For Account​ B, the simple interest earned after 30 months is ​$40.25. If the interest rate is 3.9​% for Account A and 2.3​% 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:

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P = principal

T = time in years

R = interest rate on the principal.

For account​ A, the simple interest earned after 21 months is ​$13.65. The interest rate is 3.9​% for Account A

Let y represent the principal for account B. Therefore

P = x

I = $13.65

T = 21/12 = 1.75 years

R = 3.9

Therefore

13.65 = (x × 3.9 × 1.75)/100

1365 = 6.825x

x = 1365/6.825 = $200

For account​ B, the simple interest earned after 30 months is $40.25. The interest rate is 2.3% for Account B

Let x represent the principal for account A. Therefore

P = y

I = $40.25

T = 30/12 = 2.5 years

R = 2.3

Therefore

40.25 = (y × 2.3 × 2.5)/100

4025 = 5.75y

y = 4025/5.75 = $700

The principal for account A is $200

The principal for account B is $700

For account A, interest earned in the first month is

13.65/21 = $0.65

For account B, interest earned in the first month is

40.25/30= $1.34

Account B earned the most interest in the first month(the same interest is earned every month)