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

Solve the following : Find the rate of interest compounded annually if an ordinary annuity of ₹20,000 per year amounts to ₹41,000 in 2 years.

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प्रश्न

Solve the following :

Find the rate of interest compounded annually if an ordinary annuity of ₹20,000 per year amounts to ₹41,000 in 2 years.

बेरीज
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उत्तर

Given, A = ₹41,000, C = ₹20,000, n = 2 years
We need to find r such that an ordinary annuity of ₹20,000 amounts to ₹41,000 in 2 years.

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

41,000 = `"C"/"i"[(1 + "i")^2 - 1]`

41,000 = `(20,000)/"i"[(1 + "i")^2 - 1]`

`(41,000)/(20,000)= (1 + 2"i" + "i"^2 - 1)/"i"`

`(41)/(20) = ("i"^2 + 2"i")/"i"`

`(41)/(20)` = i + 2

`(41)/(20)` – 2 = i

`(41 - 40)/(20)` = i

∴ i = `(1)/(20)` = 0.05

But i = `"r"/(100)`

∴ 0.05 = `"r"/(100)`

∴ r = 5%
The rate of interest is 5%.

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Annuity
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पाठ 2: Insurance and Annuity - Miscellaneous Exercise 2 [पृष्ठ ३१]

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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 4.17 | पृष्ठ ३१

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