To solve this problem, we need to calculate the principal amount for each account using the formula for simple interest: @Antoine_Williams
Simple Interest Formula:
I = P \times r \times t
Where:
- ( I ) is the interest earned.
- ( P ) is the principal amount (the initial amount of money).
- ( r ) is the annual interest rate (expressed as a decimal).
- ( t ) is the time the money is invested for, in years.
Account A
Given:
- Interest earned (( I )) after 3 months = $0.85
- Annual interest rate (( r )) = 3.4% or 0.034
- Time (( t )) = 3 months = 3/12 years = 0.25 years
Let’s calculate ( P ) for Account A:
0.85 = P \times 0.034 \times 0.25
To find ( P ), rearrange the formula:
P = \frac{0.85}{0.034 \times 0.25}
P = \frac{0.85}{0.0085}
P \approx 100 \, \text{(rounded to the nearest dollar)}
Account B
Given:
- Interest earned (( I )) after 27 months = $25.88
- Annual interest rate (( r )) = 2.3% or 0.023
- Time (( t )) = 27 months = 27/12 years = 2.25 years
Let’s calculate ( P ) for Account B:
25.88 = P \times 0.023 \times 2.25
Rearranging the formula gives:
P = \frac{25.88}{0.023 \times 2.25}
P = \frac{25.88}{0.05175}
P \approx 500 \, \text{(rounded to the nearest dollar)}
Determine which account earned more interest the first month
Calculate the interest earned in the first month for both accounts.
Account A Interest for 1 Month:
- I = 100 \times 0.034 \times \frac{1}{12}
I \approx 0.28
Account B Interest for 1 Month:
- I = 500 \times 0.023 \times \frac{1}{12}
I \approx 0.96
Conclusion
Account B earned more interest in the first month with approximately $0.96 compared to Account A’s $0.28.