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**Unformatted text preview: **UNSW ACTL1001 Actuarial Studies and Commerce Solutions to Tutorial Exercises 5 Exercise 1 To determine the continuous compounding (per annum) interest rate equivalent to these interest rates we use the results e δ = (1 + i ) δ = ln (1 + i ) where i is the effective p.a. interest rate and δ is the continuous compounding annual equivalent rate of interest. 1. Since e δ = (1 + i ) we have δ = ln [1 . 06] = 0 . 058269 or 5.827% p.a. 2. In this case e δ = (1 + i ) = 1 + j (2) 2 2 so that δ = 2 ln [1 . 03] = 0 . 05912 or 5.912% p.a. 3. Here e δ = (1 . 005) 12 so that δ = 12 ln [1 . 005] = 0 . 05985 or 5.985% p.a Note that all of the interest rates are nominal rates of 6% p.a. with different compounding periods. We know that the effective rate for any given nominal rate with a more frequent compounding period will be higher. This result is seen to also hold for the continuous compounding rates derived here. Note that the interest rates derived here all have the same frequency of compounding - in this case continuously. In fact insame frequency of compounding - in this case continuously....

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