Question

A person places $479 in an investment account earning an annual rate of 8.2%, compounded continuously. Using the formula V = Pe^{rt}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

Answer:

$V = 128139\ cents$

Step-by-step explanation:

Given

$V = Pe^{rt}$

$P = 479$

$r = 8.2\%$

$t = 12$

Required

Find V

To do this, we simply substitute the values of P, r and t in the above formula:

$V = Pe^{rt}$ becomes

$V = 479 * e^{8.2\% * 12}$

Convert % to decimal

$V = 479 * e^{0.082 * 12}$

$V = 479 * e^{0.984}$

$V = 479 * 2.675135411$

$V = \ 1281.38986187$

Convert to cents

$V = 1281.38986187 * 100\ cents$

$V = 128138.986187\ cents$

$V = 128139\ cents$ -- Approximated