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Answer: 5% p.a.

Amount of an immediate annuity: \(A = \dfrac{C}{i}\left[(1 + i)^n - 1\right]\), with \(C = 20000\), \(n = 2\), \(A = 41000\).

\(\dfrac{(1 + i)^2 - 1}{i} = \dfrac{2i + i^2}{i} = 2 + i\)

\(\therefore 41000 = 20000(2 + i) \Rightarrow 2 + i = 2.05 \Rightarrow i = 0.05\)

\(r = 100i = 5\). The rate of interest is 5% p.a. compounded annually.

(Check: the first instalment earns one year's interest: \(20000 \times 1.05 + 20000 = 41000\).)

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report
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