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प्रश्न
Find the present value of an annuity immediate of ₹36,000 p.a. for 3 years at 9% p.a. compounded annually. [Given (1.09)−3 = 0.7722]
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उत्तर
Given, C = ₹36,000, n = 3 years, r = 9% p.a.
∴ i = `"r"/(100) = (9)/(100)` = 0.09
Now, P = `"C"/"i"[1 - (1 + "i")^-"n"]`
= `(36,000)/(0.09)[1 - (1 + 0.09)^-3]`
= 4,00,000[1 – (1.09–3]
= 4,00,000[1 – 0.7722]
= 4,00,000(0.2278)
= 91,120
∴ Present value of the immediate annuity is ₹91,120.
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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`
