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प्रश्न
A company decides to set aside a certain sum at the end of each year to create a sinking fund, which should amount to ₹ 4 lakhs in 4 years at 10% p.a. Find the amount to be set aside each year?
[Given (1.1)4 = 1.4641]
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उत्तर
Given, A = ₹ 4,00,000, n = 4 years, r = 10% p.a, i = `"r"/100 = 10/100` = 0.1
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
∴ 4,00,000 = `"C"/0.1[(1 + 0.1)^4 - 1]`
∴ 4,00,000 × 0.1 = C[(1.1)4 − 1]
∴ 40,000 = C[1.4641 − 1]
∴ 40,000 = C(0.4641)
∴ C = `(40,000)/0.4641`
∴ C = ₹ 86,188.32
∴ The amount to be set aside each year is ₹ 2,00,000.
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A = 10,00,000 = `"C"/"I" [(1 + "i")^"n" - 1]`
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= `"C"/0.025 [1.675 - 1]`
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⇒ i = `square/100 = 4/100` = 0.04
n = Number of quarters
= 4 × 1
= `square`
⇒ P' = `(C(1 + i))/i [1 - (1 + i)^-n]`
⇒ P' = `(square(1 + square))/0.04 [1 - (square + 0.04)^-square]`
= `(2000(square))/square [1 - (square)^-4]`
= 50,000`(square)`[1 – 0.8548]
= ₹ 7,550.40
