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Question
Choose the correct alternative :
You get payments of ₹8,000 at the beginning of each year for five years at 6%, what is the value of this annuity?
Options
₹ 34,720
₹ 39,320
₹ 35,720
₹ 40,000
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Solution
P' = `("C"(1 + "i"))/"i"[1 - (1 + "i")^-"n"]`
P' = `(8000(1 + 0.06))/(0.06)[1 - (1 + 0.06)^-5]`
= `(8000(1.06))/(0.06)[1 - (1.06)^-5]`
= (1,41,333.33)(0.25274)
∴ P' = ₹35,720.
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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`
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
