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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 an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year
∴ Rate of interest per quarter = `square/4` = 4
⇒ r = 4%
⇒ i = `square/100 = 4/100` = 0.04
n = Number of quarters
= 4 × 1
= `square`
⇒ P' = `(C(1 + i))/i [1 - (1 + i)^-n]`
⇒ P' = `(square(1 + square))/0.04 [1 - (square + 0.04)^-square]`
= `(2000(square))/square [1 - (square)^-4]`
= 50,000`(square)`[1 – 0.8548]
= ₹ 7,550.40
