Question

a student wants to save $8,000 for college in 5 years how much should be put into an account that pays 5.2% annual interest compounded continuously

Answer 1

You will want to use the formula for continuously compounded interest:

$A = Pe^{rt}$

where $A$ is the resulting amount, $P$ is the initial amount, $e$ is the mathematical constant (2.718...), $r$ is the interest (in percentage), and $t$ is the time in years. Plugging these numbers into the equation gives the following:

$8000 = Pe^{0.052 * 5}$

Solving for $P$ will give you the initial amount that should be put into the account.

Answer 2

you use this formula

amount=principal(1+r%)^n
where
amount= the needed money to have been saved after five years for the                              student to join college=$8000
principal=the amount needed to be saved/invested in the account to give amount $8000 at the end of fifth year.
r=the rate of interest
therefore
$8000=p(1+5.2/100)^5
$8000=p(1+0.052)^5
$8000=p(1.052)^5
$8000=p(1.288483018284032)
$8000/(1.288483018284042)=p
$6208.851716691=p
p=$6208.8517