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Question
For an annuity immediate paid for 3 years with interest compounded at 10% p.a., the present value is ₹24,000. What will be the accumulated value after 3 years? [Given (1.1)3 = 1.331]
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Solution
Given, P = ₹24,000, n = 3 years, r = 10% p.a.
i = `"r"/(100) = (10)/(100)` = 0.1
Now, A = P(1 + i)n
= 24,000(1 + 0.1)3
= 24,000(1.1)3
= 24,000(1.331)
A = 31,944
∴ Accumulated amount after 3 years is ₹31,944.
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∴ 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]`
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= 50,000`(square)`[1 – 0.8548]
= ₹ 7,550.40
