Question

You have 2 different savings accounts. For Account​ A, the simple interest earned after 9 months is ​$5.40. For Account​ B, the simple interest earned after 18 months is ​$18.00. If the interest rate is ​3.6% 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.

a) Principal for Account A: $1,200, Principal for Account B: $750, Account A earned more interest.
b) Principal for Account A: $1,500, Principal for Account B: $750, Account A earned more interest.
c) Principal for Account A: $1,000, Principal for Account B: $750, Account B earned more interest.
d) Principal for Account A: $1,000, Principal for Account B: $1,500, Account B earned more interest.

Answer 1

Account A has a principal of $200 and Account B has a principal of $500. In the first month, Account B earned more interest than Account A.

Step-by-step explanation:

The question involves calculating the principal amount in two different savings accounts using the formula for simple interest: I = PRT, where I is interest, P is principal, R is the annual interest rate (in decimal), and T is the time in years. To solve for the principal (P), you rearrange the formula to P = I / (RT).

For Account A with a simple interest of $5.40 after 9 months (0.75 years) at an annual interest rate of 3.6% (0.036), the principal is P = $5.40 / (0.036 * 0.75) = $200. For Account B with $18.00 after 18 months (1.5 years) at 2.4% (0.024), the principal is P = $18.00 / (0.024 * 1.5) = $500.

To determine which account earned more interest in the first month, we calculate the monthly interest for each account (using 1/12 of the annual rate). Account A earns $200 * (0.036 / 12) = $0.60 per month, and Account B earns $500 * (0.024 / 12) = $1.00 per month. Hence, Account B earned more interest in the first month.