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Old 11-28-2017, 10:57 PM
David_Mo David_Mo is offline
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Question Annuity with Payment in Geometric Progressions

"On January 1, 1988, Felix inherited a perpetuity with annual payments beginning in six months. The first payment was $3,000, and after that the payments increased by 3% each year. Find the value of this perpetuity on January 1, 1995 if the annual effective interest rate was 6% from January 1, 1988 through January 1, 1996 and 4% thereafter."

I don't how to handle this kind of question, could anyone please help me out with that? the final answer is $397,388.55
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Old 11-28-2017, 11:07 PM
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Gandalf Gandalf is offline
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Using formulas for geometric series, you should be able to calculate the value of the payments starting July 1, 1997 on July 1, 1997. Then discount that to January 1, 1995.

Separately, calculate the value of the payments for July 1, 1988 to July 1, 1996 on July 1, 1988. Then accumulate that to January 1, 1995.
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Old 11-29-2017, 03:01 AM
David_Mo David_Mo is offline
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Is that how I calculate the value of the payments starting July 1, 1997?

3000(1.06)^7.5[1-(1.03/1.06)^8/1-(1.03/1.06)]
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Old 11-30-2017, 01:27 AM
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I don't know what formula you are trying to apply there, but if you are just trying to calculate the value of payments after July 1, 1997 (and are trying to get the value on January 1, 1995 [you didn't say what date your value was on]), there should be almost no use of the 6% interest rate.

You can get the value on July 1, 1997 with no use of 6%, and it gets used for only one year in discounting to Jan 1, 1995.
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