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Old 05-12-2019, 09:32 AM
xkang1129 xkang1129 is offline
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Default 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!
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Old 05-12-2019, 09:45 AM
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Gandalf Gandalf is offline
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Quote:
Originally Posted by xkang1129 View Post
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!
You are using a nominal rate of 3% instead of a real rate of 3%.
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Old 05-12-2019, 10:06 AM
xkang1129 xkang1129 is offline
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Ahh! got it!! Many thanks, Gandalf!
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Old 05-12-2019, 11:14 AM
xkang1129 xkang1129 is offline
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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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