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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]
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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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`
