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Find the accumulated value of annuity due of ₹1,000 p.a. for 3 years at 10% p.a. compounded annually. [Given (1.1)3 = 1.331] - Mathematics and Statistics

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प्रश्न

Find the accumulated value of annuity due of ₹1,000 p.a. for 3 years at 10% p.a. compounded annually. [Given (1.1)3 = 1.331]

योग
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उत्तर

Given C = ₹1,000, n = 3 years, r = 10% p.a.

∴ i = `"r"/(100) = (10)/(100)` = 0.1

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

∴ A = `(1,000(1 + 0.1))/(0.1)[(1 + 0.1)^3 - 1]`

= `(1,000(1.1))/(0.1)[(1.1)^3 - 1]`

= (1,000)(11)[1.331 – 1]
= 11,000(0.331)
∴ A = 3,641
∴ Accumulated value of annuity due is ₹3,641.

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Insurance and Annuity - Exercise 2.2 [पृष्ठ २८]

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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 1.11 | पृष्ठ २८

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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

∴ 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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