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प्रश्न
Find the number of years for which an annuity of ₹500 is paid at the end of every year, if the accumulated amount works out to be ₹1,655 when interest is compounded annually at 10% p.a.
उत्तर
Given, C = ₹500, A = ₹1,655, r = 10% p.a.
∴ i = `"r"/(100) = (10)/(100)` = 0.1
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
∴ 1,655 = `(500)/(0.1)[(1 + 0.1)^"n" - 1]`
∴ `((1,655)(0.1))/(500)` = (1.1)n – 1
∴ 0.331= (1.1)n – 1
∴ (1.1)n = 1 + 0.331
∴ (1.1)n = 1.331
∴ (1.1)n = (1.1)3
∴ n = 3
∴ The annuity is paid for 3 years.
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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`
