Final answer:
To find the future value of $1690 invested at 7.2% interest compounded continuously after 8 years, we use the formula V = Pert. The calculation gives us approximately $3008.14, which is the amount to the nearest cent in the account after 8 years.
Step-by-step explanation:
Given that a person places $1690 in an investment account with an annual rate of 7.2% compounded continuously, we can use the formula V = Pert to find the future value of this investment after 8 years. Here, V is the future value, P is the principal amount ($1690), e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (0.072 as a decimal), and t is the time in years.
To solve for V, we plug in the known values:
We calculate:
V = 1690 * e^(0.072 * 8)
Using a calculator, we can find the value of e raised to the power of (0.072 * 8), and then multiply by 1690 to get the future value of the investment.
Therefore, the amount of money in the account to the nearest cent after 8 years would be:
V ≈ $1690 * 2.71828^(0.576) ≈ $1690 * 1.77928953 ≈ $3008.14.