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Find accumulated value after 1 year of an annuity immediate in which ₹ 10,000 is invested every quarter at 16% p.a. compounded quarterly. [Given (1.04)4 = 1.1699] - Mathematics and Statistics

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Question

Find accumulated value after 1 year of an annuity immediate in which ₹ 10,000 is invested every quarter at 16% p.a. compounded quarterly. [Given (1.04)4 = 1.1699]

Sum
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Solution

Given, C = ₹ 10,000
Amount is invested every quarter for one year.
∴ n = 4
Rate of interest is 16% p.a
∴ r = `(16)/(4)` = 4%

i = `"r"/(100) = (4)/(100)` = 0.04

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

= `(10,000)/(0.04)[(1 + 0.04)^4 - 1]`

= `(10,000 xx 100)/(0.04 xx100)[(1.04)^4 - 1]`

= `(10,00,000)/4(1.1699 - 1)`

= 2,50,000 × 0.1699

= 42,475

∴ Amount accumulated value after 1 years is ₹ 42,475.

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Annuity
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Chapter 2: Insurance and Annuity - Exercise 2.2 [Page 27]

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The future amount, A = ₹ 10,00,000

Period, n = 20, r = 5%, (1.025)20 = 1.675

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

I = `5/200` = `square` as interest is calculated semi-annually

A = 10,00,000 = `"C"/"I" [(1 + "i")^"n" - 1]`

10,00,000 = `"C"/0.025 [(1 + 0.025)^square - 1]`

= `"C"/0.025 [1.675 - 1]`

10,00,000 = `("C" xx 0.675)/0.025`

C = ₹ `square`


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