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Question
Find the amount of an ordinary annuity if a payment of ₹ 500 is made at the end of every quarter for 5 years at the rate of 12% per annum compounded quarterly. [Given (1.03)20 = 1.8061]
Solution
Given, C = ₹ 500
Amount is invested at the end of every quarter.
∴ It is an immediate annuity.
Rate of interest is 12% p.a.
∴ r = `(12)/(4)`% = 3% per quarter
∴ i = `"r"/(100) = (3)/(100)` 0..03
The period is of 5 years and payment is made on quarterly basis.
∴ n = 5 x 4 = 20
Since, A = `"C"/"i"[(1 + "i")^"n" - 1]`
= `(500)/(0.03)[(1 + 0.03)^20 - 1]`
= `(500)/(0.03)[(1.03)^20 - 1]`
= `(500)/(0.03)(1.8061 - 1)`
= `(500)/(0.03) xx (0.8061)`
= `(403.05)/(0.03)`
= `(40305)/(3)`
= ₹ 13,435
∴ Amount of ordinary annuity is ₹ 13,435.
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[Given (1.1)4 = 1.4641]
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`
