To find the difference between the two accounts at the end of 4 years, we'll calculate the total amount in each account and then determine the difference.
Account 1: Simple Interest
The formula for simple interest is:
\[ A = P(1 + rt) \]
Where:
- \(A\) is the total amount after time \(t\),
- \(P\) is the principal amount (initial deposit),
- \(r\) is the annual interest rate (as a decimal),
- \(t\) is the time in years.
For Account 1:
- \(P = 1200\)
- \(r = 0.015\) (1.5% as a decimal)
- \(t = 4\)
Plugging the values into the formula:
\[ A_1 = 1200(1 + 0.015 \times 4) \] \[ A_1 = 1200(1 + 0.06) \] \[ A_1 = 1200 \times 1.06 \] \[ A_1 = 1272 \]
Account 2: Compounded Interest
The formula for compound interest is:
\[ A = P(1 + r)^t \]
For Account 2:
- \(P = 1200\)
- \(r = 0.015\)
- \(t = 4\)
Plugging the values into the formula:
\[ A_2 = 1200(1 + 0.015)^4 \] \[ A_2 = 1200(1.015)^4 \]
Calculating \(1.015^4\):
\[ 1.015^4 \approx 1.061364 \]
Now plugging this value back into the equation:
\[ A_2 \approx 1200 \times 1.061364 \] \[ A_2 \approx 1273.64 \]
Difference Between the Accounts
Now we find the difference between Account 2 and Account 1:
\[ \text{Difference} = A_2 - A_1 \approx 1273.64 - 1272 = 1.64 \]
Thus, the difference between the two accounts at the end of 4 years is approximately $1.64.