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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`
The future amount, A = ₹ 10,00,000
Period, n = 20, r = 5%, (1.025)20 = 1.675
A = `"C"/"I" [(1 + "i")^"n" - 1]`
I = `5/200` = `square` as interest is calculated semi-annually
A = 10,00,000 = `"C"/"I" [(1 + "i")^"n" - 1]`
10,00,000 = `"C"/0.025 [(1 + 0.025)^square - 1]`
= `"C"/0.025 [1.675 - 1]`
10,00,000 = `("C" xx 0.675)/0.025`
C = ₹ `square`
