How much would you need to depost in an account now in order

How much would you need to depost in an account now in order to have $4000 in the account in 15 years? Assume the account earns 5% interest compounded continuously.

Solution

Given that

Amount A = $4000

Time t = 15 years

Annual interest rate r = 5 % = 0.05

Initial amount to deposit = P

We know that

Compound intersest continuously is ,

A = Pe^rt

4000 = P.e^(0.05)15

   P = 4000 / ( e^(0.05)15 )

P = $1889.47

Therefore,

Amount to deposit = $1889.47