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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.
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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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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`
