Final answer:
To find Cyndie's initial investment, we can use the formula for compound interest: A = P * e^(rt), where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.718), r is the interest rate (in decimal form), and t is the time in years. We are given that after 6 years, Cyndie has $1691.25. Using the formula and simplifying the expression gives us the initial investment: P = $1500.
Step-by-step explanation:
To find Cyndie's initial investment, we can use the formula for compound interest: A = P * e^(rt), where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.718), r is the interest rate (in decimal form), and t is the time in years. We are given that after 6 years, Cyndie has $1691.25. Substituting these values into the formula:
1691.25 = P * e^(0.02 * 6)
Using a calculator, we can evaluate e^(0.02 * 6) to get approximately 1.127. Rearranging the equation:
P = 1691.25 / 1.127
Simplifying this expression gives us the initial investment:
P = $1500