Question A person places $$ \$ 26200 $$ in an investment account earning an annual rate of $$ 3.2 \% $$, compounded continuously, Using the formula $$ V=P e^{r t} $$, 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 2o years.

Question

UpStudy AI · Accepted Answer

To determine the amount of money in the account after 20 years, we can use the formula for continuous compounding:

$$ V = P e^{r t} $$

Given:
- $$ P = \$26200 $$ (initial investment)
- $$ r = 3.2\% = 0.032 $$ (annual rate of interest)
- $$ t = 20 $$ years

Substitute the given values into the formula:

$$ V = 26200 \times e^{0.032 \times 20} $$

Now, we can calculate the value of $$ V $$ using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$26200e^{0.032\times 20}$$
- step1: Multiply the numbers:
  $$26200e^{0.64}$$
- step2: Convert the expressions:
  $$26200e^{\frac{16}{25}}$$
- step3: Rewrite the expression:
  $$26200\sqrt[25]{e^{16}}$$
The amount of money in the account after 20 years is approximately $49687.80 to the nearest cent.
The amount of money in the account after 20 years is approximately \$49,687.80.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Calculus Questions