Question

A person places $6340 in an investment account earning an annual rate of 8.4%, compounded continuously. Using the formula V = P e 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 2 years.

Answer 1

Answer:

$7499.82

Step-by-step explanation:

We have been given that a person places $6340 in an investment account earning an annual rate of 8.4%, compounded continuously. We are asked to find amount of money in the account after 2 years.

We will use continuous compounding formula to solve our given problem as:

$A=Pe^{rt}$, where

A = Final amount after t years,

P = Principal initially invested,

e = base of a natural logarithm,

r = Rate of interest in decimal form.  

$8.4\%=\frac{8.4}{100}=\frac{8.4}{100}=0.084$

Upon substituting our given values in above formula, we will get:

$A=\ 6340\cdot e^{0.084\cdot 2}$

$A=\ 6340\cdot e^{0.168}$

$A=\ 6340\cdot 1.1829366106478107$

$A=\ 7499.818111507119838$

Upon rounding to nearest cent, we will get:

$A\approx \ 7499.82$

Therefore, an amount of $7499.82 will be in account after 2 years.