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Question
Find the present value of an ordinary annuity of ₹63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given (1.14)−4 = 0.5921]
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Solution
Given, C = 63,000, n = 4 years, r = 14% p.a.
∴ i = `"r"/(100) (14)/(100)` = 0.14
Now, P = `"C"/"i" [1 - (1 + "i")^-"n"]`
= `(63000)/(0.14)[1 - (1 + 0.14)^-4]`
= 4,50,000[1 – (1.14)–4]
= 4,50,000[1 – 0.5921]
= 4,50,000(0.4079)
= 1,83,555
∴ Present value of an ordinary annuity is ₹1,83,555.
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For annuity due,
C = ₹ 20,000, n = 3, I = 0.1, (1.1)–3 = 0.7513
Therefore, P = `square/0.1 xx [1 - (1 + 0.1)^square]`
= 2,00,000 [1 – 0.7513]
= ₹ `square`
