Question

5a how much more interest is earned from investing $700 at a compound interest rate of 2.5% for 7 years than from investing $700 at a simple interest rate for 2.5% for 7 years? (round to the nearest cent if necessary).

Explanation:

Step1: Calculate Simple Interest

The formula for simple interest is \( I_{simple} = P \times r \times t \), where \( P = 700 \), \( r = 0.025 \), and \( t = 7 \).
\( I_{simple} = 700 \times 0.025 \times 7 = 700 \times 0.175 = 122.5 \)

Step2: Calculate Compound Interest

The formula for compound interest is \( A = P(1 + r)^t \), so the interest \( I_{compound} = A - P = P(1 + r)^t - P \).
Substitute \( P = 700 \), \( r = 0.025 \), \( t = 7 \):
\( A = 700(1 + 0.025)^7 \)
First, calculate \( (1.025)^7 \approx 1.185994 \)
Then, \( A \approx 700 \times 1.185994 \approx 830.1958 \)
\( I_{compound} \approx 830.1958 - 700 = 130.1958 \)

Step3: Find the Difference

Subtract the simple interest from the compound interest:
\( Difference = I_{compound} - I_{simple} \approx 130.1958 - 122.5 = 7.6958 \)
Round to the nearest cent: \( 7.70 \) (or \( 7.7 \) if we consider one decimal, but since it's cents, two decimals)

Answer:

\(\$7.70\)