The question is using rule 72 determine Kari wants to save 10,000 for a down payment on a house. Illustrate the difference in years it will take her to double her current 5,000 savings based on 6%, 12% and 18% interest rate .

To find the difference in years it will take Kari to double her current savings based on different interest rates, we will use the rule of 72 formula.

The rule of 72 states that the approximate number of years it takes to double an investment is equal to 72 divided by the annual interest rate.

Let's calculate the difference in years for each interest rate:

1. For an interest rate of 6%:
Using the rule of 72 formula, we have: \frac{72}{6} = \text{number of years}
Simplifying, we find: \text{number of years} = 12 years.

2. For an interest rate of 12%:
Using the rule of 72 formula, we have: \frac{72}{12} = \text{number of years}
Simplifying, we find: \text{number of years} = 6 years.

3. For an interest rate of 18%:
Using the rule of 72 formula, we have: \frac{72}{18} = \text{number of years}
Simplifying, we find: \text{number of years} = 4 years.

Therefore, the difference in years it will take Kari to double her current $5,000 savings based on 6%, 12%, and 18% interest rates is:
- 12 years for a 6% interest rate,
- 6 years for a 12% interest rate, and
- 4 years for an 18% interest rate.

Answer: The difference in years for Kari to double her current $5,000 savings is 12 years at 6%, 6 years at 12%, and 4 years at 18% interest rate.