Step 1 :Given that the principal amount (P) is \$1000, the total amount to be paid back is \$1645, and the time (T) is 3 years.
Step 2 :We can find the interest (I) by subtracting the principal from the total amount to be paid back, which is \$1645 - \$1000 = \$645.
Step 3 :The formula for simple interest is \(I = PRT\), where I is the interest, P is the principal amount, R is the rate of interest, and T is the time.
Step 4 :We can rearrange the formula to solve for R: \(R = \frac{I}{PT}\).
Step 5 :Substituting the given values into the formula, we get \(R = \frac{645}{1000 \times 3} = 0.215\).
Step 6 :To convert this to a percentage, we multiply by 100, which gives us \(0.215 \times 100 = 21.5\%\).
Step 7 :Final Answer: The simple interest rate is \(\boxed{21.5\%}\).