To find the higher resulting balance between simple interest and compound interest for an amount of $500 invested over a period of 10 years, we can calculate both separately.
Simple Interest Calculation
The formula for simple interest is:
\[ A = P(1 + rt) \]
where:
- \( A \) is the final amount
- \( P \) is the principal amount (initial investment)
- \( r \) is the rate of interest (as a decimal)
- \( t \) is the time in years
Given:
- \( P = 500 \)
- \( r = 0.08 \) (8%)
- \( t = 10 \)
Now, plugging in these values:
\[ A = 500(1 + 0.08 \times 10) = 500(1 + 0.8) = 500 \times 1.8 = 900 \]
Compound Interest Calculation
The formula for compound interest is:
\[ A = P(1 + r)^t \]
where:
- \( A \) is the final amount
- \( P \) is the principal amount (initial investment)
- \( r \) is the rate of interest (as a decimal)
- \( t \) is the time in years
Given:
- \( P = 500 \)
- \( r = 0.09 \) (9%)
- \( t = 10 \)
Now, plugging in these values:
\[ A = 500(1 + 0.09)^{10} = 500(1.09)^{10} \]
Now we need to calculate \( (1.09)^{10} \):
Using a calculator:
\[ (1.09)^{10} \approx 2.36736 \]
Now we can find \( A \):
\[ A \approx 500 \times 2.36736 \approx 1183.68 \]
Result Comparison
- Simple Interest Result: \( 900 \)
- Compound Interest Result: \( 1183.68 \)
The higher resulting balance after investing $500 for 10 years is $1183.68.