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Question
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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Solution
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 annuity due,
C = ₹ 20,000, n = 3, I = 0.1, (1.1)–3 = 0.7513
Therefore, P = `square/0.1 xx [1 - (1 + 0.1)^square]`
= 2,00,000 [1 – 0.7513]
= ₹ `square`
