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प्रश्न
Find the present value of an ordinary annuity of ₹63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given (1.14)−4 = 0.5921]
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उत्तर
Given, C = 63,000, n = 4 years, r = 14% p.a.
∴ i = `"r"/(100) (14)/(100)` = 0.14
Now, P = `"C"/"i" [1 - (1 + "i")^-"n"]`
= `(63000)/(0.14)[1 - (1 + 0.14)^-4]`
= 4,50,000[1 – (1.14)–4]
= 4,50,000[1 – 0.5921]
= 4,50,000(0.4079)
= 1,83,555
∴ Present value of an ordinary annuity is ₹1,83,555.
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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]`
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= `"C"/0.025 [1.675 - 1]`
10,00,000 = `("C" xx 0.675)/0.025`
C = ₹ `square`
