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?

Use the continuous compound interest formula: A = Pert

Answer 1

$584.88

Explanation:

If $396 is invested at an interest rate of 13% per year and is compounded continuously in 3 years.

Formula of continuous compound interest :
`A=Pe^(rt)`

Where

A = Future Amount

P = Principal amount ( $396.00 )

r = rate of interest 13% ( 0.13 )

t = time in years (3 years)

Now put the values in the formula

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

`A=396(2.718282^(0.39))`

= 396 (1.476981)

= 584.884394 ≈ 584.88

The amount after 3 years would be $584.88

Answer 2

`A=\$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`