Marvin, aged 50, purchases an annuity of k per month, the first payment to be made immediately. For the first 60 months, payments will be guaranteed (i.e., will be made independent of Marvin's survival). After that, payments will continue for as long as Marvin is alive. Marvin pays 50,000 for the entire package.

Let i = .07, Dso = 5200, Dss =4100, and Nss = 60,000. Find k.