Question

how long will it take for $1000 to double at a simple interest rate of 5.5%?
how much will five dozen oranges cost?

Explanation:

Step1: Recall Simple Interest Formula

The simple interest formula is $A = P(1 + rt)$, where $A$ is the final amount, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. We want the money to double, so $A = 2P$. Substituting $A = 2P$ into the formula gives $2P = P(1 + rt)$.

Step2: Simplify the Equation

Divide both sides of $2P = P(1 + rt)$ by $P$ (assuming $P
eq0$), we get $2 = 1 + rt$. Then subtract 1 from both sides: $rt = 1$.

Step3: Substitute the Interest Rate

The interest rate $r$ is $5.5\%$ or $0.055$ in decimal. Substitute $r = 0.055$ into $rt = 1$, we have $0.055t = 1$.

Step4: Solve for t

Divide both sides by $0.055$: $t=\frac{1}{0.055}\approx18.18$ years.

Answer:

Approximately 18.18 years