On December 31, 2008 your company estimates that it will pay $10 million in 2009 and subsequent years on claims incurred in 2008 and prior years. It expects the payout pattern to be as follows:

Year Cumulative payments

2008 60%

2009 80%

2010 90%

2012 100%

Determine the duration (both Macaulay and Modified) of the claims payments assuming that they are paid at the end of each calendar year and the effective interest rate is 10%.