Warren would like to accumulate $$1,600$ in a bank account by depositing monthly

payments of a fixed size into the account $($at the end of each month$),$ which pays a certain

rate of interest compounded monthly.

Warren calculates the number of payments that will be required, and arrives at an answer

of $27\mathrm{.}2.$ He decides to deal with the fact that this is not a whole number by making a

balloon payment. This means that:

Warren will make $27$ monthly payments and at some point between the end of the

$27$th month and the end of the $28$th month he will deposit the difference between

$$1,600$ and what he has accumulated up to that point.

Warren will make $28$ monthly payments in order to deliberately accumulate more

than he originally required.

Warren will make $27$ monthly payments and on the day of the $27$th payment, he

will deposit the difference between $$1,600$ and what he has accumulated up to that

point.

Warren will make $27$ monthly payments, and allow these payments to accumulate

to the end of the $28$th month. At that time, he will deposit the difference between

$$1,600$ and what he has accumulated up to that point.

Warren will make $28$ monthly payments and get a refund of the overage a month

later.