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Find the present value of an ordinary annuity of ₹63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given (1.14)−4 = 0.5921] - Mathematics and Statistics

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प्रश्न

Find the present value of an ordinary annuity of ₹63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given (1.14)−4 = 0.5921]

योग
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उत्तर

Given, C = 63,000, n = 4 years, r = 14% p.a.

∴ i = `"r"/(100)  (14)/(100)` = 0.14

Now, P = `"C"/"i" [1 - (1 + "i")^-"n"]`

= `(63000)/(0.14)[1 - (1 + 0.14)^-4]`

= 4,50,000[1 – (1.14)–4]
= 4,50,000[1 – 0.5921]
= 4,50,000(0.4079)
= 1,83,555
∴ Present value of an ordinary annuity is ₹1,83,555.

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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 1.06 | पृष्ठ २७

संबंधित प्रश्न

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[Given (1.1)4 = 1.4641]


For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year

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⇒ r = 4%

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= 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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