Question

You have 2 different savings accounts. For Account​ A, the simple interest earned after 21 months is ​$6.65. For Account​ B, the simple interest earned after 27 months is ​$23.63. If the interest rate is ​3.8% for Account A and ​2.1% 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

The principal in Account A is $200 and in Account B is $1,000. Account B earned more interest in the first month, with $1.75 compared to Account A's $0.63.

Step-by-step explanation:

To calculate the principal for each account, we can use the formula for simple interest: I = PRT, where I is the interest earned, P is the principal, R is the annual interest rate, and T is the time in years. For Account A, we have an interest of $6.65, an annual rate of 3.8%, and a time of 21 months (or 21/12 years). For Account B, we have an interest of $23.63, an annual rate of 2.1%, and a time of 27 months (or 27/12 years).

For Account A: $6.65 = P * 0.038 * (21/12)
For Account B: $23.63 = P * 0.021 * (27/12)

Solving these equations, we get:
Account A Principal: $6.65 / (0.038 * (21/12)) = $200
Account B Principal: $23.63 / (0.021 * (27/12)) = $1,000

To determine which account earned the most interest in the first month, we calculate the monthly interest for each account using the principal amounts we found:

Account A: $200 * 0.038 / 12 = $0.63
Account B: $1,000 * 0.021 / 12 = $1.75

Therefore, Account B earned more interest in the first month.