Skill: 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)$.