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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]
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 x 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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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`
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
