How much must one invest today in order to receive $$p after $t years if interest is compounded continuously at the rate r = $r%?
If P0 dollars are deposited into an account earning interest at an annual rate r compounded continuously, then the value of the account after t years is .
The desired value of the account after $t years is $$p, or P($t) = 3jRAm4T6Mr4=.
Interest is compounded continuously at a rate of $r%, so we let r = R7MvkioXBvw= .
Using , express P($t) in terms of P0.
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Since P($t) = $p, we have $p = P0e$u.
Solve for P0 rounded to the nearest cent.
$p = P0e$u.
P0 ≈ $qjqZz1N+poo=