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प्रश्न
Solve the following :
Find the least number of years for which an annuity of ₹3,000 per annum must run in order that its amount exceeds ₹60,000 at 10% compounded annually. [(1.1)11 = 2.8531, (1.1)12 = 3.1384]
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उत्तर
Given, C = ₹3,000, A = ₹60,000, r = 10% p.a.
∴ i = `"r"/(100) = (10)/(100)` = 0.1
Since, A = `"C"/"i"[(1 + "i")^"n" - 1]`
∴ 60,000 = `(3,000)/(0.1)[(1 + 0.1)^"n" - 1]`
∴ `(60,000 xx 0.1)/(3,000)` = (1.1)n – 1
∴ 2 = (1.1)n – 1
∴ (1.1)n = 2 + 1
∴ (1.1)n = 3
It is given that (1.1)11 = 2.8531 and (1.1)12 = 3.1384
∴ n will be between 11 years and 12 years.
Thus, the least number of years for which an annuity of ₹3,000 per annum must run is 12 years.
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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]`
10,00,000 = `"C"/0.025 [(1 + 0.025)^square - 1]`
= `"C"/0.025 [1.675 - 1]`
10,00,000 = `("C" xx 0.675)/0.025`
C = ₹ `square`
