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प्रश्न
A person wants to create a fund of ₹ 6,96,150 after 4 years at the time of his retirement. He decides to invest a fixed amount at the end of every year in a bank that offers him interest of 10% p.a. compounded annually. What amount should he invest every year? [Given (1.1)4 = 1.4641]
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उत्तर
Given, A = ₹ 6,96,150, n = 4 years, r = 10% p.a.
i = `"r"/(100) = (10)/(100)` = 0.1
Now, A = `"C"/"i" [(1 + "i")^"n" - 1]`
∴ 6,96,150 = `"C"/(0.1)[(1 + 0.1)^4 - 1]`
∴ 6,96,150 × 0.1 = C[(1.1)4 – 1]
∴ 69,615 = C[1.4641 – 1]
∴ 69,615 = C(0.4641)
∴ C = `(69, 615)/(0.4641)`
∴ C = 1,50,000
∴ Sum of ₹ 1,50,000 should be invested every year.
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[Given (1.1)4 = 1.4641]
For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year
∴ Rate of interest per quarter = `square/4` = 4
⇒ r = 4%
⇒ 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
