A deferred annuity is an annuity which delays its payouts. This means that the payouts do not start until after a certain duration. Notice that a deferred annuity is just a deposit at the start, followed by an annuity. Your task is to define a Higher-order Function that returns a function that takes in a given interest rate and outputs the amount of money that is left in a deferred annuity.

Define a function new_balance(principal, gap, payout, duration) that returns a single-parameter function which takes in a monthly interest rate and outputs the balance in a deferred annuity. gap is the duration in months before the first payment, payout is monthly and duration is just the total number of payouts. Written in Python code.



Test Case:
new_balance(1000, 2, 100, 2)(0.1)
Output:
1121.0