Cooper invests money in an account paying simple interest. He invests $\$ 150$ and no money is added or removed from the investment. After one year, he has $\$ 156$ . What is the simple percent interest per year? $\newline$ Answer:________ $\%$

Full solution

Q. Cooper invests money in an account paying simple interest. He invests

\$ 150

and no money is added or removed from the investment. After one year, he has

\$ 156

. What is the simple percent interest per year?

\newline

Answer:________

\%

Identify principal, total amount, interest: Identify the principal, the total amount after one year, and the interest earned. $\newline$ The principal (initial investment) is $\$150$ . After one year, the total amount is $\$156$ . The interest earned is the total amount after one year minus the principal. $\newline$ Interest = Total amount after one year - Principal $\newline$ Interest = $\$156 - \$150$ $\newline$ Interest = $\$6$
Use simple interest formula: Use the formula for simple interest to find the rate. $\newline$ The formula for simple interest is $I = PRT$ , where $I$ is the interest, $P$ is the principal, $R$ is the rate, and $T$ is the time in years. We need to solve for $R$ (the rate). $\newline$ We know that $I = \$6$ , $P = \$150$ , and $T = 1$ year. Plugging these values into the formula gives us: $\newline$ $\$6 = \$150 \times R \times 1$
Solve for rate: Solve for R (the rate). $\newline$ To find R, we divide both sides of the equation by $\$150$ : $\newline$ $R = \frac{\$6}{\$150}$ $\newline$ $R = 0.04$
Convert rate to percentage: Convert the decimal rate to a percentage. $\newline$ To convert a decimal to a percentage, we multiply by $100$ . $\newline$ Rate as a percentage = $R \times 100$ $\newline$ Rate as a percentage = $0.04 \times 100$ $\newline$ Rate as a percentage = $4\%$