To determine the higher resulting balance between simple interest and compounded interest, we can calculate both.
Simple Interest Calculation
Simple interest is calculated using the formula: \[ A = P(1 + rt) \] where:
- \( A \) = total amount after interest
- \( P \) = principal amount (initial investment)
- \( r \) = annual interest rate (as a decimal)
- \( t \) = time in years
For our scenario:
- \( P = 500 \)
- \( r = 0.08 \) (8%)
- \( t = 10 \)
Substituting these values into the formula: \[ A = 500(1 + 0.08 \cdot 10) \] \[ A = 500(1 + 0.8) \] \[ A = 500(1.8) \] \[ A = 900 \]
Compound Interest Calculation
Compound interest is calculated using the formula: \[ A = P(1 + r)^t \] where:
- \( A \) = total amount after interest
- \( P \) = principal amount (initial investment)
- \( r \) = annual interest rate (as a decimal)
- \( t \) = time in years
For our scenario:
- \( P = 500 \)
- \( r = 0.09 \) (9%)
- \( t = 10 \)
Substituting these values into the formula: \[ A = 500(1 + 0.09)^{10} \] \[ A = 500(1.09)^{10} \]
Calculating \( (1.09)^{10} \): \[ (1.09)^{10} \approx 2.367364 \] Now substituting this value back into the formula: \[ A \approx 500 \times 2.367364 \approx 1183.68 \]
Comparison of Balances
- Simple interest balance after 10 years: $900
- Compound interest balance after 10 years: $1183.68
Final Answer
The higher resulting balance after investing $500 for a period of 10 years is: \[ \text{\textbf{The higher resulting balance is }} $1183.68 \]
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