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Question
A lady plans to save for her daughter’s marriage. She wishes to accumulate a sum of ₹ 4,64,100 at the end of 4 years. What amount should she invest every year if she gets an interest of 10% p.a. compounded annually? [Given (1.1)4 = 1.4641]
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Solution
Given: A = ₹ 4,64,100, n = 4 years, r = 10% p.a.
i = `r/(100) = (10)/(100)` = 0.1
Now, A = `C/i[(1 + i)^n - 1]`
∴ 4,64,100 = `C/(0.1)[(1 + 0.1)^4 - 1]`
∴ 4,64,100 × (0.1) = C[(1.1)4 – 1]
∴ 46,410 = C[1.4641 – 1]
∴ 46,410 = C(0.4641)
∴ C = `(46,410)/(0.4641)`
∴ C = 1,00,000
∴ She must invest ₹ 1,00,000 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`
