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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]
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`
