Actuarial Outpost Annuity with Payment in Geometric Progressions
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#1
11-28-2017, 10:57 PM
 David_Mo SOA Join Date: Nov 2017 Posts: 4
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."

#2
11-28-2017, 11:07 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 30,980

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.
#3
11-29-2017, 03:01 AM
 David_Mo SOA Join Date: Nov 2017 Posts: 4

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)]
#4
11-30-2017, 01:27 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 30,980

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.