Net premiums earned increased for  2012 compared to 2011 primarily due to increases in direct premiums earned as a  result of an increase in NIW and a decrease in premiums refunded in connection with rescissions in 2012 compared to 201 1.  The increase in net premiums earned in 2012 was partially offset by an increase in ceded premiums earned related to the  Reinsurance Transactions. (See “ Reinsurance ” below.) Net premiums earned decreased in 2011 compared to 2010 due to a  decrease in our insurance in force and an increase in the premiums refunded in connection with rescissions in  2011 compared to  2010. This decrease in premiums earned was partially of fset by a decrease in ceded premiums resulting from the termination  and run-off of captive reinsurance arrangements. Our projected rate of return on our single premium business is lower than on our monthly premium business.  Assuming  all other factors remain constant, if loans prepay earlier than expected, then our profitability on these single premium loans is  likely to be higher than anticipated. If loans are repaid later than expected, our profitability on these single premium loans is  likely to be lower than anticipated. The expected profitability of our monthly premium business is the opposite of single  premium business with respect to prepayment speeds with earlier than anticipated prepayments reducing profitability on these  monthly premium loans. As a result, the ultimate profitability of our business is dependent in part on mortgage prepayment  speeds. Because prepayment speeds are dif ficult to project, we believe a mixture of single premium and monthly premium  business is desirable to protect against actual prepayment speeds that are significantly dif ferent from expectations.  The following table provides additional information related to mortgage insurance premiums written and earned for the  years indicated: Reinsurance.  In the second quarter of 2012, Radian Guaranty entered into a quota share reinsurance agreement with a  third-party reinsurance provider (the “Initial Quota Share Reinsurance  Transaction”). Through the Initial Quota Share  Reinsurance Transaction, Radian Guaranty agreed to cede 20% of its NIW  beginning with the business written in the fourth  quarter of 2011. As of December 31, 2012, the amount ceded pursuant to the Initial Quota Share Reinsurance  Transaction was  $1.5 billion of Radian Guaranty’ s RIF. Radian Guaranty has the ability to commute two-thirds of the reinsurance ceded as part  of this transaction on December 31, 2014, which would result in Radian Guaranty reassuming the related RIF in exchange for  payment of a predefined commutation amount from the reinsurer .  Under the Initial Quota Share Reinsurance  Transaction, for the year ended December 31, 2012, ceded premiums written  were $52.2 million and ceded premiums earned were $16.1 million. Ceding commissions earned under the Initial Quota Share  Reinsurance Transaction for the year ended December 31, 2012 were $13.0 million. In the fourth quarter of 2012, Radian Guaranty and the same third-party reinsurance provider agreed to a second quota  share reinsurance agreement (the “Second Quota Share Reinsurance  Transaction” and together with the Initial Quota Share  Reinsurance Transaction, the “Reinsurance Transactions”) that provides for additional ceded risk of $750 million initially and  up to a maximum of $2 billion upon the mutual agreement of the parties.  As of December 31, 2012, the amount ceded pursuant  to the Second Quota Share Reinsurance Transaction was $368.4 million of Radian Guaranty’ s RIF.  The agreed upon terms also provide that, ef fective as of December 31, 2015, Radian Guaranty will have the ability , at its  option (the “Commutation Option”), to commute one-half of the reinsurance ceded with respect to conventional GSE loans,  which would result in Radian Guaranty reassuming the related RIF in exchange for a payment of a predefined commutation  amount from the reinsurer . Pursuant to the agreed upon terms: 102 Year Ended December 31, (In thousands) 2012 2011 2010 Net premiums written Primary and pool insurance. . . . . . . . . . . . . . . . . . . . . $ 804,371 $ 715,125 $ 698,078 Second-lien mortgages (“Second-liens”) . . . . . . . . . . 1,874 2,314 1,535 International . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 (175 ) 296 Net premiums written-insurance. . . . . . . . . . . . . . . . . . . . $ 806,305 $ 717,264 $ 699,909 Net premiums earned Primary and pool insurance. . . . . . . . . . . . . . . . . . . . . $ 699,079 $ 673,869 $ 727,484 Second-liens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,874 2,314 2,501 International . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,432 4,712 9,646 Net premiums earned-insurance. . . . . . . . . . . . . . . . . . . . . $ 702,385 $ 680,895 $ 739,631