how much I must deposit now in a 12% account (annual interest) if I want to be able to withdraw $20 000 at the end of each of the next five years.
Hello, gusty!
There is a formula for this very problem, but we can derive the formula ourselvesHow much I must deposit now in a 12% account (annual interest)
if I want to be able to withdraw $20,000 at the end of each of the next five years?
. . if we're willing to invest some time and effort.
Let = amount of our initial deposit.
End of year-1: its value grows to dollars,
. . and $20,000 is withdrawn.
The balance is: .
End of year-2: the value grows to ,
. . and $20,000 is withdrawn.
The balance is: .
End of year-3: the value grows to
. . and $20,000 is withdrawn.
The balance is: .
End of year-4: the value grows to
. . and $20,000 is withdrawn.
The balance is: .
End of year-5: the value grows to
When the final $20,000 is withdrawn, the balance is zero.
. .
. . .[1]
On the right, we have a geometric series with: .
. . Its sum is: .
Substitute into [1]: .
Therefore: .