Question

The term of the annuity certain is increased to 30 years, along with an appropriate adjustment to the claims paid for the premium of $500,000 to ensure the Actual Reserves at Year 30 are zero. Calculate the Actual Reserves at Year 27 (to the nearest whole dollar), assuming the interest rate remains at 5% per annum.

Answer 1

ANSWER:

	Annuity payment=	P/ [ [1- (1+r)-n ]/r ]
P=	Investment	500,000.00

Rate of interest per period
Rate of interest per annum	5.0%
Payments per year	1.00
Rate of interest per period	5.000%

n=	number of payments:
	Number of years	30
	Payments per year	1.00
	number of payments	30

Annuity payment=	500000/ [ (1- (1+0.05)^-30)/0.05 ]
Annuity payment=	32,525.72

At year 27, only 3 years of payments remain.

a

Present value of annuity=

P* [ [1- (1+r)-n ]/r ]

P=	Periodic payment	32,525.72
r=	Rate of interest per period
	Annual interest	5.00%
	Number of payments per year	1
	Interest rate per period	0.05/1=
	Interest rate per period	5.000%

n=	number of periods:
	Number of years	3
	Periods per year	1
	number of payments	3

Present value of annuity=	32525.7175401383* [ (1- (1+0.05)^-3)/0.05 ]
Present value of annuity=	88,575.60

Value of reserves at year 27 is 88,575.60

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