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प्रश्न
Find the rate of interest compounded annually if an annuity immediate at ₹20,000 per year amounts to ₹2,60,000 in 3 years.
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उत्तर
Given, C = ₹20,000, A = ₹2,60,000, n = 3 years.
Now, A = `"C"/"i"[(1 + "I")^"n" - 1]`
∴ 2,60,000 = `(20,000)/"i"[(1 + "i")^3 - 1]`
∴ `(2,60,000)/(20,000) = (1)/"i" [1 + 3"i" + 3"i"^2 + "i"^3 - 1]`
∴ 13 = `(3"i" + 3"i"^2 + "i"^3)/"i"`
∴ 13 = 3 + 3i + i2
∴ i2 + 3i – 10 = 0
∴ i2 + 5i – 2i – 10 = 0
∴ i(i + 5) – 2(i + 5) = 0
∴ (i + 5)(i – 2) = 0
∴ i = – 5 or i = 2
But, i cannot be negative.
∴ i = 2
∴ `"r"/(100)` = 2
∴ r = 200% p.a.
∴ The rate of interest is 200% p.a.
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For annuity due,
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Therefore, P = `square/0.1 xx [1 - (1 + 0.1)^square]`
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= ₹ `square`
