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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]
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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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[Given (1.1)4 = 1.4641]
For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year
∴ 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]`
⇒ P' = `(square(1 + square))/0.04 [1 - (square + 0.04)^-square]`
= `(2000(square))/square [1 - (square)^-4]`
= 50,000`(square)`[1 – 0.8548]
= ₹ 7,550.40
