Question

a student invests $1,000 at a 5% simple interest rate for 4 years. the formula for simple interest is i = prt. if the student increases the time to 6 years while keeping the principal and rate the same, how will the interest earned change?

Explanation:

Step1: Recall Simple Interest Formula

The simple interest formula is \( I = Prt \), where \( P \) is principal, \( r \) is rate, \( t \) is time.

Step2: Calculate Interest for 4 Years

Given \( P = 1000 \), \( r = 5\% = 0.05 \), \( t_1 = 4 \).
\( I_1 = 1000 \times 0.05 \times 4 = 200 \).

Step3: Calculate Interest for 6 Years

\( t_2 = 6 \), so \( I_2 = 1000 \times 0.05 \times 6 = 300 \).

Step4: Analyze the Change

Compare \( I_1 \) and \( I_2 \). \( I_2 - I_1 = 300 - 200 = 100 \). Alternatively, since \( P \) and \( r \) are constant, \( I \) is proportional to \( t \). The time increases from 4 to 6 (a factor of \( \frac{6}{4} = 1.5 \)), so interest also increases by the same factor (from 200 to 300, which is \( 200 \times 1.5 = 300 \)). So interest increases.

Answer:

The interest earned will increase (from $200 to $300, or by a factor of 1.5) because simple interest is directly proportional to time when principal and rate are constant.