Final answer:
Myra will have approximately $2173.91 in her account after 10 years, which is calculated using the formula for continuous compounding, where the initial deposit is $800 and the money doubles every 7.3 years.
Step-by-step explanation:
Myra deposited $800 into an account with continuous compounding, where money doubles every 7.3 years. Using the rule of 72, we can calculate the rate of interest by dividing 72 by the number of years it takes to double, which is 7.3. This gives us an interest rate of approximately 9.86% (72/7.3).
To find out how much money Myra will have after 10 years, we use the formula for continuous compounding, A = Pert, where P is the initial principal ($800), r is the rate of interest (0.0986 as a decimal), e is the base of the natural logarithms, and t is the time in years (10).
Therefore, the total amount after 10 years will be:
A = 800e0.0986×10
To get the number, you must calculate 800 multiplied by e raised to the power of (0.0986 times 10). Using a calculator, we get A ≈ $2173.91
So, to the nearest dollar and cents, Myra will have $2173.91 in her account after 10 years.