To find the higher resulting balance between simple interest at 8% and compound interest at 9%, we will calculate the future value for both scenarios.
Simple Interest Calculation
The formula for simple interest is: \[ A = P(1 + rt) \] where:
- \( A \) is the future value,
- \( P \) is the principal amount ($500),
- \( r \) is the rate of interest (8% or 0.08),
- \( t \) is the time in years (10 years).
Plugging in the values: \[ A = 500(1 + 0.08 \times 10) = 500(1 + 0.8) = 500 \times 1.8 = 900 \]
So, the balance with simple interest is $900.00.
Compound Interest Calculation
The formula for compound interest is: \[ A = P(1 + r)^t \] where:
- \( A \) is the future value,
- \( P \) is the principal amount ($500),
- \( r \) is the rate of interest (9% or 0.09),
- \( t \) is the time in years (10 years).
Plugging in the values: \[ A = 500(1 + 0.09)^{10} = 500(1.09)^{10} \] Calculating \( (1.09)^{10} \): \[ (1.09)^{10} \approx 2.36736 \] Now calculating \( A \): \[ A \approx 500 \times 2.36736 \approx 1183.68 \]
So, the balance with compound interest is $1183.68.
Conclusion
Comparing both balances:
- Simple Interest: $900.00
- Compound Interest: $1183.68
Thus, the higher resulting balance after investing $500 for a period of 10 years is $1183.68.
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