To compare the amounts earned in both accounts, we can calculate the total amount for Account A (simple interest) and Account B (compound interest) separately after 5 years.
Account A: Simple Interest
The formula for calculating simple interest is:
\[ A = P + (P \times r \times t) \]
Where:
- \(A\) is the total amount (principal + interest)
- \(P\) is the principal amount (initial deposit)
- \(r\) is the annual interest rate (in decimal)
- \(t\) is the time (in years)
For Account A:
- \(P = 350\)
- \(r = 0.06\)
- \(t = 5\)
Substituting the values into the formula:
\[ A = 350 + (350 \times 0.06 \times 5) \]
Calculating the interest:
\[ A = 350 + (350 \times 0.3) = 350 + 105 = 455 \]
So, the total amount in Account A after 5 years is $455.
Account B: Compound Interest
The formula for calculating compound interest is:
\[ A = P \times (1 + r)^t \]
Where:
- \(A\) is the total amount (principal + interest)
- \(P\) is the principal amount (initial deposit)
- \(r\) is the annual interest rate (in decimal)
- \(t\) is the time (in years)
For Account B:
- \(P = 350\)
- \(r = 0.06\)
- \(t = 5\)
Substituting the values into the formula:
\[ A = 350 \times (1 + 0.06)^5 \]
Calculating:
\[ A = 350 \times (1.06)^5 \] \[ A = 350 \times 1.338225 \] \[ A \approx 467.38 \]
So, the total amount in Account B after 5 years is approximately $467.38.
Comparing the two accounts
Now, let's find out how much more Account B earns compared to Account A:
\[ \text{Difference} = A_B - A_A = 467.38 - 455 = 12.38 \]
Conclusion
Account B (compound interest) earns approximately $467.38, while Account A (simple interest) earns $455. Therefore, Account B earns $12.38 more than Account A after 5 years.
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