Question

If $396 is invested at an interest rate of 13% per year and is compounded continuously, how much will the investment be worth in 3 years? (A, right?)

$584.88

$583.66

$581.27

$268.11

Answer 1

yay

continously



`A=Pe^(rt)`

A=future amount
P=princiapl=invested
r=rate in decimal
t=time in years

so

given P=396
r=13%=0.13
t=3


`A=396e^((0.13)(3))`

`A=396e^(0.39)`
use calculator
A=$584.88

answer is first option
ya, you aer right

Answer 2

`\$584.88`

Explanation:

we know that

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

`t=3\ years\\ P=\$396\\ r=0.13`

substitute in the formula above

`A=\$396(e)^(0.13*3)=\$584.88`