A person places $934 in an investment account earning an annual rate of 6.1%, compounded continuously. Using the formula V = P n r t 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 13 years.

Step-by-step explanation:

The formula for continuously compounded interest is

V = P x e (r x t)

Where

V represents the future value of the account after t years.

P represents the principal or initial amount invested

e is the base of a natural logarithm,

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = $934

r = 6.1% = 6.1/100 = 0.061

t = 13 years

Therefore,

V = 934 e (0.061 x 13)

V = 934 e (0.793)

V = $2064.2 to the nearest cent

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