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Question
Find the accumulated (future) value of annuity of ₹ 800 for 3 years at interest rate 8% compounded annually. [Given (1.08)3 = 1.2597]
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Solution
Given, C = ₹ 800, n = 3 years, r = 8% p.a.
i = `"r"/(100) = (8)/(100)` = 0.08
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
∴ A = `(800)/(0.08)[(1 + 0.08)^3 - 1]`
= `(800 xx 100)/(0.08 xx 100)[(1.08)^3 - 1]`
= `(80000)/8(1.2597 - 1)`
= 10,000 × 0.2597
= 2,597
∴ Accumulate (future) value of annuity is ₹ 2,597.
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For annuity due,
C = ₹ 20,000, n = 3, I = 0.1, (1.1)–3 = 0.7513
Therefore, P = `square/0.1 xx [1 - (1 + 0.1)^square]`
= 2,00,000 [1 – 0.7513]
= ₹ `square`
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`
