Question

A person places $84800 in an investment account earning an annual rate of 4. 1%,

compounded continuously. Using the formula V = Pert, where Vis 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

$~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \ 84800\\ r=rate\to 4.1\%\to \frac{4.1}{100}\dotfill &0.041\\ t=years\dotfill &4 \end{cases} \\\\\\ A=84800e^{0.041\cdot 4}\implies A=84800e^{0.01025}\implies A\approx 85673.67$

Answer 2

The amount that will be in the account after 4 years is $99912.57

Exponential functions

The standard expoenential functions is expressed as:

V . = Pe^rt

Given the following

P = $84800

r = 4.1% = 0.041

t =4years

Substititute

V = 84800e^4(0.041)

V = 84800e^0.164

V = $99912.57

Hence the amount that will be in the account after 4 years is $99912.57

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