ACTSC231Tutorial4

# ACTSC231Tutorial4 - if i = 3 and j = 4.5 3 A continuously...

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ACTSC 231 Tutorial 4 Nov 10, 2009 1. It is reported that the present value of an annuity paying \$1,000 at the end of each year for Y years is \$12,692.58 and the present value of an annuity paying \$300 at the end of each year for four years is \$1,069.12. Find the present value of an annuity paying \$500 at the end of every second year for Y years. 2. You receive a 10-year annuity paying \$100 at the end of each quarter for the first four years, and \$35 at the end of each month for the remaining six years. Express the value at the time of the last payment in terms of annuity symbols introduced this past week if the annual effective rate is i for the first four years and j for the following six years. Evaluate
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Unformatted text preview: if i = 3% and j = 4.5%. 3. A continuously paying level annuity pays \$50 each year for ten years. The force of interest at time t is t = 2/(1 + 2t). a) Find the present value of this annuity. b) If instead of \$50 per year, the rate of payment at time t is 1 + 4t + 4t 2 , find the present value of this annuity. 4. Consider a continuously increasing annuity for n periods in which payments are being made continuously at rate t at time t. Effective interest rate per period is i. Find an expression for the present value of this annuity, and a logical notation for it....
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