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प्रश्न
Solve the following :
Find the present value of an annuity immediate of ₹20,000 per annum for 3 years at 10% p.a. compounded annually. [(1.1)–3 = 0.7513]
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उत्तर
Given, C = ₹20,000, n = 3 years, r = 10 % p.a.
∴ i = `"r"/(100) = (10)/(100)` = 0.1
Since, P = `"C"/"i"[1 - (1 + "i")^"n"]`
∴ P= `(20,000)/(0.1)[1 - (1 + 0.1)^-3]`
= 2,00,000[1 – (1.1)–3]
= 2,00,000[1 – 0.7513]
= 2,00,000(0.2487)
= ₹49,740
∴ Present value of an annuity immediate is ₹49,740.
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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`
