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FM inflation/geometric annuity problem help
Can someone help me with this question?
Suppose you are the actuary for an insurance company. Your company, in response to a policyholder claim involving physical injury, is responsible for making annual medical payments. The first payment will occur on January 1, 2008, and the final payment will occur on January 1, 2031. The first payment will be $100,000; after that, the payments will increase annually for inflation, at a rate of 5% per year. The real interest rate is 3% per year. Find the present value of these future payments as of December 31, 2005. Correct Answer: 1,491,363 My solution (yields the wrong answer, not sure where went wrong): Payments: 100,000 unit, 1, 1.05, 1.05^2, 1.05^3, ... 1.05^23 PV as of January 1, 2007: 100,000 ( v + 1.05V^2 + 1.05^2V^3......1.05^23V^24) = 100,000 V * S24(at 1.94%, 1.94=1.05/1.03) = 2,932,053.088 PV as of December 31, 2005: 2,932,053.088 * V = 2,932,053.088 / 1.03 = 2,846,653.483 Can someone help point out where I did wrong please? Many thanks! 
#2




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#4




Correct solution:
Nominal rate: 1.05 * 1.03  1 = 0.0815 Payments: 100,000 unit, 1, 1.05, 1.05^2, 1.05^3, ... 1.05^23 PV as of January 1, 2007: 100,000 ( v + 1.05V^2 + 1.05^2V^3......1.05^23V^24) (at 8.15%) = 100,000 V(8.15%) * a24(at 3%, 1/(1.05/1.0815)) = 1,612,908.8 PV as of December 31, 2005: 1,612,908.8 * V = 1,612,908.8 / 1.0815 = 1.4913627 
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geometric series 
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