A person places $26300 in an investment account earning an annual rate of 3.8%, 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 19 years.

V = $ 54135.92

Step-by-step explanation:

The formula for compounding continuously is given as:

V = P(e)^rt

V = Amount of money in the bank after 19 years

P = Principal amount initially invested = $26300

e = base of natural log

r = Interest rate = 3.8% = 0.038

t = time in years = 19

We have to calculate the value of V. Substitute all values into the given formula:

V = P(e)^rt

V = (26300)(e)^(0.038 · 19)

V = (26300)(2.718)^(0.722)

V = (26300)(2.0584)

V = $ 54135.92

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