The loan is paid with equal payments during 100 periods (each payment is made in the end of the corresponding period), and the interest rate per period is 0.02. For the payment made in period 81, what part of it is made towards principal payment?
(Your answer should be a number between 0 and 1, with 0.001 precision: the total payment -- 1 -- is divided to a payment towards interest accrued on the remaining principal during this period, say \lambda\in\left[0,1\right] λ∈[0,1], and a principal payment, 1-\lambda1−λ).