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Question
Find the present value of an annuity due of ₹ 600 to be paid quarterly at 32% p.a. compounded quarterly. [Given (1.08)−4 = 0.7350]
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Solution
Given: C = ₹ 600,
Amount is invested every quarter for one year.
∴ n = 4
Rate of interest is 32% p.a.
∴ r = `(32)/(4)` = 8%
i = `"r"/(100) = (8)/(100)` = 0.08
Now, P' = `("C"(1 + "i"))/"i"[1 - (1 + "i")^-"n"]`
∴ P' = `(600(1 + 0.08))/(0.08)[1 - (1 + 0.08)^-4]`
= `(600(1.08))/(0.08)[1 - (1.08)^-4]`
= (7,500)(1.08)[1 – 0.7350]
= 8,100 × 0.2650
P' = 2,146.5
∴ Present value of annuity due is ₹ 2,146.5.
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∴ Rate of interest per quarter = `square/4` = 4
⇒ r = 4%
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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]`
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