1. a) State the simple interest formula. __ b) 500 is invested in a 3-year term deposit that pays 2.5% simple interest. What is the principal (P or PV)? c) Calculate the interest earned on the investment in part b). d) How much interest would have been earned if the investment had a 6-month term? e) How many years would it take for the 500 investment to double in value? 2. When interest earned is added to the principal and left invested, the result is called __

## Step 1: State the simple interest formula<br />### The simple interest formula is given by $I = Prt$, where $I$ is the interest earned, $P$ is the principal, $r$ is the interest rate (as a decimal), and $t$ is the time in years.<br /><br />## Step 2: Identify the principal<br />### The principal is the initial amount invested, which is given as $500. So, $P = \$500$.<br /><br />## Step 3: Calculate the interest earned over 3 years<br />### We have $P = \$500$, $r = 2.5\% = 0.025$, and $t = 3$ years. Using the formula $I = Prt$, we get $I = 500 \times 0.025 \times 3 = \$37.50$.<br /><br />## Step 4: Calculate the interest earned over 6 months<br />### 6 months is equivalent to $\frac{6}{12} = 0.5$ years. Using the formula $I = Prt$ with $t = 0.5$, we get $I = 500 \times 0.025 \times 0.5 = \$6.25$.<br /><br />## Step 5: Calculate the time to double the investment<br />### To double the investment, the interest earned must equal the principal. So, $I = P$. We have $I = Prt$, so $P = Prt$. Dividing both sides by $P$, we get $1 = rt$. We want to find $t$, so $t = \frac{1}{r} = \frac{1}{0.025} = 40$ years.<br /><br />## Step 6: Define compound interest<br />### When interest earned is added to the principal and left invested, the result is called compound interest.