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Question
A person sets up a sinking fund in order to have ₹ 1,00,000 after 10 years. What amount should be deposited bi-annually in the account that pays him 5% p.a. compounded semi-annually? [Given (1.025)20 = 1.675]
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Solution
Given A = ₹ 1,00,000
Amount is deposited bi-annually for 10 years.
∴ n = 10 × 2 = 20
Rate of intererst is 5% p.a.
∴ r = `(5)/(2)`% = 2.5%
i = `"r"/(100) = (2.5)/(100)` = 0.025
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
∴ 1,00,000 = `"C"/(0.025)[(1 + 0.025)^20 - 1]`
∴ 1,00,000 = `"C"/(0.025)[(1.025)^20 - 1]`
∴ (1,00,000)(0.025) = C[(1.025)20 – 1]
∴ 2,500 = C[1.675 – 1]
∴ 2,500 = C(0.675)
∴ C = `(2,500)/(0.675)` = 3,703.70
∴ Amount of ₹ 3,703.70 should be deposited bi-annually into the account.
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Therefore, P = `square/0.1 xx [1 - (1 + 0.1)^square]`
= 2,00,000 [1 – 0.7513]
= ₹ `square`
