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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Solve the following : After how many years would an annuity due of ₹3,000 p.a. accumulated ₹19,324.80 at 20% p. a. compounded yearly? [Given (1.2)4 = 2.0736] - Mathematics and Statistics

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प्रश्न

Solve the following :

After how many years would an annuity due of ₹3,000 p.a. accumulated ₹19,324.80 at 20% p. a. compounded yearly? [Given (1.2)4 = 2.0736]

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उत्तर

Given, C = ₹3,000, A' = 19324.80, r = 20% p.a.

∴ i = `"r"/(100) = (20)/(100)` = 0.2

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

∴ 19,324.80 = `(3,000(1 + 0.2))/(0.2) [(1 + 0.2)^"n" - 1]`

∴ 19,324.80 = `(3,000 xx 1.2)/(0.2) [(1.2)^"n" - 1]`

∴ 19,324.80 = 3,000 x 6 [(1.2)n – 1]

∴ `(19,324.80)/(18,000)` = (1.2)n  – 1

∴ `(19,32,480)/(18,000 xx 100)` = (1.2)n  – 1

∴ `(1,07,360)/(1,00,000)` = (1.2)n  – 1

∴ 1.0736 = (1.2)n  – 1
∴ (1.2) = 1.0736 + 1
∴ (1.2) = 2.0736
∴ (1.2) = (1.2)4       ...[ `Theta` (1.2)4 = 2.0736]
∴ n = 4 years
∴ After 4 years, an annuity due of ₹3,000 p.a. would accumulate to ₹19,324.80 at 20% p.a. compounded annually.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Insurance and Annuity - Miscellaneous Exercise 2 [पृष्ठ ३२]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 2 Insurance and Annuity
Miscellaneous Exercise 2 | Q 4.23 | पृष्ठ ३२

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