Actuarial Outpost PV of Perp Due with tricky interest rates
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#1
02-06-2020, 10:25 PM
 DionysusOfZero SOA Join Date: Dec 2019 College: University of Minnesota Alumni Posts: 5
PV of Perp Due with tricky interest rates

They say the perpetuity due with annual payments of 15,000 where i = .1 for the 1st 10 years and .08 thereafter can be found using the attached formula.

I tried 15,000(a(umlauts)10,.1 + (1/.08)v^10), but this did not yield the correct answer of 179,457.87

Can anyone explain why my method didn't work.
Also looking to understand the formula they used, it isn't registering with me as something that makes sense.

Thanks a ton! I test the 18th.
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#2
02-06-2020, 10:37 PM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 5,705

The second term in your brackets should be 1.08/0.08 * v^10, where v uses 10%. The 1.08 adjusts for beginning of period payments.
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#3
02-06-2020, 10:43 PM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 5,705

And the listed formula is adding a perpetuity immediate to the payment of \$15,000 at time 0. The perpetuity immediate uses 10% throughout, but adds in the difference between 8% and 10%, all discounted for 10 years at 10%.
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