Question

How long will it take to double your savings if you earn 6.9 percent interest, compounded annually? Multiple Choice 11.39 years 1117 years 12.02 years 10.39 years 11.89 years

Answer 1

To double your savings with a 6.9 percent interest rate, it will take around 10.43 years using the rule of 72.

Step-by-step explanation:

To determine how long it will take to double your savings with a 6.9 percent interest rate, you can use the rule of 72. The rule of 72 states that you divide 72 by the interest rate to find the approximate number of years it takes for an investment to double. In this case, dividing 72 by 6.9 gives you approximately 10.43. Therefore, it will take around 10.43 years to double your savings with a 6.9 percent interest rate.

Answer 2

Using the Rule of 72, it's estimated to take approximately 10.43 years for savings to double with a 6.9% interest rate. Due to the choices given, 10.39 years is the closest option after an exact calculation.

Step-by-step explanation:

The concept in question deals with compound interest and how quickly an investment can grow under certain conditions, specifically relating to savings. To determine how long it will take to double an investment with a 6.9 percent interest rate, compounded annually, we can use the Rule of 72. The Rule of 72 is a simplified formula to estimate the number of years required to double the invested money at a fixed annual rate of interest. You divide 72 by the interest rate to find out how many years it will take for your savings to double.

Using the Rule of 72: 72 ÷ 6.9 = approximately 10.43 years

However, since that number is not one of the options provided, we should do the exact calculation with the following compound interest formula: A = P(1 + r/n)^(nt). To solve for 't' when A/P is 2 (since we want to double the investment), we have:

2 = (1 + 0.069/1)^(1*t), we find that t ≈ 10.24 years. Therefore, the closest answer provided in the options is 10.39 years, which is the best estimate considering the calculations made.