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Question
A person invested ₹ 5,000 every year in finance company that offered him interest compounded at 10% p.a., what is the amount accumulated after 4 years? [Given (1.1)4 = 1.4641]
Solution
Given, C = ₹ 5,000, r = 10%p.a., n = 4 years
i = `"r"/100 = 10/100` = 0.1
It is an immediate annuity.
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
= `(5,000)/(0.1)[1 + 0.1^4 - 1]`
= 50,000[(1.1)4 – 1]
= 50,000[1.4641 – 1]
= 50,000(0.4641)
= 23,205
∴ Amount accumulated after 4 years is ₹ 23,205.
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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`
