Question

1. janice also received $5,000. she put the money into a savings account at 2 percent interest. how long will it take to double her money?

Explanation:

Step1: Use Rule of 72 approximation

The Rule of 72 estimates time to double money: $\text{Time} = \frac{72}{\text{Interest Rate}}$

Step2: Plug in 2% interest rate

$\text{Time} = \frac{72}{2}$

Answer:

36 years

*Note: For precise calculation using compound interest formula $A = P(1+r)^t$ where $A=2P$, $r=0.02$:

Step1: Set up compound interest equation

$2P = P(1+0.02)^t$

Step2: Simplify equation

$2 = (1.02)^t$

Step3: Solve for t with logarithm

$t = \frac{\ln(2)}{\ln(1.02)}$

Step4: Calculate value

$t \approx \frac{0.6931}{0.0198} \approx 35$ years

The Rule of 72 provides a quick approximation, while the precise compound interest calculation gives ~35 years. The Rule of 72 is a common shortcut for this type of problem.*