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प्रश्न
Solve the following :
A company decides to set aside a certain amount at the end of every year to create a sinking fund that should amount to ₹9,28,200 in 4 years at 10% p.a. Find the amount to be set aside every year. [(1.1)4 = 1.4641]
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उत्तर
Given, A = ₹9,28,200, n = 4 years, r = 10% p.a, i = `"r"/(100) = (10)/(100)` = 0.1
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
∴ 9,28,200 = `"C"/(0.1)[(1 + 0.1)^4 - 1]`
∴ 9,28,200 x 0.1 = C[(1.1)4 – 1]
∴ 92,820 = C[1.4641 – 1]
∴ 92,820 = C(0.4641)
∴ C = `(92,820)/(0.4641)`
∴ C = ₹2,00,000
∴ The amount to be set aside each year is ₹2,00,000.
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[Given (1.1)4 = 1.4641]
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`
