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ACTSC 231 ch04-eg-soln

# ACTSC 231 ch04-eg-soln - Example 4.1 Suppose an annuity...

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Example 4.1 Example 4.1: Suppose an annuity pays \$1000 every 5 years for 35 years. The rate of interest is 5% per year effective. Find the present value and the accumulation value at the expiration date for a) payments in advance; b) payments in arrear. C. Weng ([email protected]) – p. 2/1

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Example 4.2 Example 4.2: Suppose an annuity pays \$100 every month for 15 years. The interest rate is 5% per year effective. Find the present value of the annuity for a) payments in advance b) payments in arrear C. Weng ([email protected]) – p. 4/1
Continuous constant annuities Consider an annuity of \$1 per period payable continuously for n periods. Assume the effective interest rate is i per period. Present value is denoted by ¯ a n . Formulae: ¯ a n = 1 - v n δ , where δ is the equivalent constant force of interest corresponding to the interest rate i and hence δ = ln(1 + i ) . Accumulated value is denoted by ¯ s n : XBox ¯ s n = (1 + i ) n ¯ a n = (1 + i ) n - 1 δ = dispvarint n 0 e t dt Relations: lim m →∞ ä

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