Question

A person places $8290 in an investment account earning an annual rate of 6%, compounded continuously. Using the formula =V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 12 years.

Answer 1

The amount of money in the account after 12 years, with a principal of $8290 and an annual interest rate of 6%, compounded continuously, is approximately $16356.86.

Step-by-step explanation:

To find the amount of money in the account after 12 years, we can use the formula V = Pe^(rt), where V is the value of the account, P is the principal initially invested, e is the base of a natural logarithm, r is the rate of interest, and t is the time in years. In this case, the principal (P) is $8290, the rate of interest (r) is 6%, and the time (t) is 12 years.

Plugging in these values, we have V = 8290 * e^(0.06*12). Using a calculator, we find that e^(0.06*12) is approximately 1.974. Multiplying this by 8290, we get V = 8290 * 1.974 = $16356.86.

Therefore, the amount of money in the account after 12 years is approximately $16356.86.

Answer 2

Step-by-step explanation:

Using the formula V = Pe^(rt), where P is the principal initially invested, e is the base of a natural logarithm, r is the rate of interest, and t is the time in years:

V = Pe^(rt)

We are given that P = $8290, r = 0.06 (since the annual interest rate is 6%), and t = 12 (since we want to find the value of the account after 12 years). Therefore, we can plug in these values and solve for V:

V = 8290 * e^(0.06*12)

V = 8290 * e^(0.72)

V = $17,936.34

Therefore, the amount of money in the account after 12 years, to the nearest cent, is $17,936.34.