Final answer:
To find the missing values assuming continuously compounded interest, we can use the formula for compound interest. We can calculate the initial investment, determine the annual % rate, find the time to double the investment, and calculate the amount after a given time period.
The correct option is not given.
Step-by-step explanation:
To find the missing values assuming continuously compounded interest, we can use the formula for compound interest:
Future Value = Principal x (1 + interest rate)^time
A) To calculate the initial investment, we can rearrange the formula as:
Principal = Future Value / (1 + interest rate)^time
For example, if the amount after 10 years is $750, we can substitute the values into the formula:
Principal = $750 / (1 + interest rate)^10
B) To determine the annual % rate, we need to use logarithms to solve for the interest rate:
interest rate = (Future Value / Principal)^(1/time) - 1
Using the values from part A, we can substitute them into the formula to calculate the annual % rate.
C) To find the time to double the investment, we need to rearrange the formula as:
time = log(Base, (Future Value / Principal))
Using the given values, we can calculate the time it takes to double the investment.
D) To calculate the amount after 10 years, we can use the formula:
Amount = Principal x (1 + interest rate)^time
Substituting the values into the formula, we can calculate the amount after 10 years.
The correct option is not given.