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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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[Given (1.1)4 = 1.4641]
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`
