Consider a deferred perpetuity that pays you $500,000 every 6 months, however, the first payment happens only 30 months (i.e., 2.5 years from now). Assume all spot rates are equal to each other and denote them by r

Lets denote the original perpetuity by S1. Consider three other perpetuities: S2 that pays $500,000 every six months starting one year from, S3 that pays $1,000,000 every six months starting 1 year from now, and S4 that pays $250,000 every six months starting 1 year from now. Let D1, D2, D3, and D4 be durations of these perpetuities. Assume all spot rates are equal to each other but not necessarily equal to 8%. Rank the Durations of these four perpetuities from lowest to highest (if some or all of them are equal, make sure to say so too). No explanation is necessary.