Compare simple interest earned over different periods

Simple interest is determined by $I=Prt$ , where $P$ is principal, $r$ the annual rate expressed as a decimal, and $t$ time in years; comparing investments or loans involves interpreting how changes in principal, rate, or period affect interest, while distinguishing interest earned from the final amount $P+I$ . Comparisons use proportional reasoning, including time conversions such as months to years, and exclude compounding, variable rates, and complex irregular schedules.

Detailed Explanation: Compare simple interest earned over different periods

To compare simple interest for different periods, use

I=Prt

where:

$P$ is the principal, or starting amount,
$r$ is the annual interest rate written as a decimal,
$t$ is the time in years.

If time is given in months, convert it to years:

\text{time in years}=\frac{\text{number of months}}{12}

Example: Two investments each start with 600 $and earn$ (4%)$ simple interest per year.

Investment A lasts $8$ months.
Investment B lasts $(14)$ months.

Which investment earns more interest, and how much more?

Investment A

First convert $8$ months to years:

t=\frac{8}{12}=\frac{2}{3}\text{ year}

Write $(4\%)$ as a decimal:

r=0.04

Now substitute into the simple interest formula:

I=600(0.04)\left(\frac{2}{3}\right)

I=\$16

Investment A earns 16$ in interest.

Investment B

Convert $(14)$ months to years:

t=\frac{14}{12}=\frac{7}{6}\text{ years}

Use the formula again:

I=600(0.04)\left(\frac{7}{6}\right)

I=\$28

Investment B earns 28$ in interest.

Therefore, Investment B earns more:

\$28-\$16=\$12

Answer: Investment B earns 12$ more interest than Investment A.

The comparison is about interest earned, not the final amount. The final amounts would be 616 $and$ $628 $, because final amount equals$ (P+I)$.

Learn by doing: Compare simple interest earned over different periods

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Interest (Simple) - Change in Interest from Change in Time (All Values, Relative)

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