Simple Interest - Pre Algebra

1. What formula gives the total amount $A$ in an account after simple interest is added?

   $A = P + Prt$, which can also be written $A = P(1 + rt)$.

2. In $I = Prt$, what does the principal $P$ represent?

   The original amount of money invested or borrowed, before any interest is added.

3. In $I = Prt$, in what form must the rate $r$ be entered?

   As a decimal (or fraction). For example, $5\%$ is entered as $0.05$, not 5.

4. A loan lasts 18 months. What value of $t$ is used in $I = Prt$?

   $t = 1.5$. Time must be in years, and $18 \div 12 = 1.5$.

5. What is the simple interest on 500 dollars at $4\%$ per year for 3 years?

   60 dollars. $I = 500 \times 0.04 \times 3 = 60$.

6. What is the simple interest on 800 dollars at $2.5\%$ per year for 4 years?

   80 dollars. $800 \times 0.025 = 20$ per year, and $20 \times 4 = 80$.

7. How many years does 400 dollars at $5\%$ simple interest take to earn 100 dollars in interest?

   5 years. $t = \frac{I}{Pr} = \frac{100}{400 \times 0.05} = 5$.

8. What is the simple interest formula, and what does each variable mean?

   $I = Prt$: $I$ is interest, $P$ is principal, $r$ is the annual rate as a decimal and $t$ is time in years.

9. An account starts with 1,000 dollars and earns $5\%$ simple interest per year. What is the balance after 2 years?

   1,100 dollars. The interest is $1000 \times 0.05 \times 2 = 100$, added to the principal.

10. How does simple interest differ from compound interest?

    Simple interest is computed only on the original principal, so the interest earned is the same every year.

11. An investment of 200 dollars earns 30 dollars of simple interest in 3 years. What is the annual rate?

    $5\%$. $r = \frac{I}{Pt} = \frac{30}{200 \times 3} = 0.05$.

12. What is the simple interest on 2,000 dollars at $3\%$ per year for 6 months?

    30 dollars. Six months is $t = 0.5$ years: $2000 \times 0.03 \times 0.5 = 30$.

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