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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] - Mathematics and Statistics

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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]

योग
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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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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Insurance and Annuity - Exercise 2.2 [पृष्ठ २७]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 2 Insurance and Annuity
Exercise 2.2 | Q 1.05 | पृष्ठ २७

संबंधित प्रश्न

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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


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