Question

A person places $4080 in an investment account earning an annual rate of 5.7%, 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 4 years.

Answer 1

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:

, where

A = Final amount after t years,

P = Principal initially invested,

e = base of a natural logarithm,

r = Rate of interest in decimal form.

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

Upon rounding to nearest cent, we will get:

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

Answer 2

5124.83

Explanation:

r=5.7\%=0.057

r=5.7%=0.057

Move decimal over two places

P=4080

P=4080

Given as the pricipal

t=4

t=4

Given as the time

V=Pe^{rt}

V=Pe

rt

V=4080e^{0.057( 4)}

V=4080e

0.057(4)

Plug in

V=4080e^{0.228}

V=4080e

0.228

Multiply

V=5124.8281\approx 5124.83

V=5124.8281≈5124.83