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Question
Find the value of (1.01)5, correct up to three places of decimals.
Solution
(1.01)5 = (1 + 0.01)5
= 5C0(1)5 + 5C1(1)4(0.01) + 5C2(1)3(0.01)2 + 5C3(1)2(0.01)3 + 5C4(1)(0.01)4 + 5C5(0.01)5
Now, 5C0 = 1 = 5C5
5C1 = 5 = 5C4
5C2 = `(5 xx 4)/(1 xx 2)` = 10 = 5C3
∴ (1.01)5 = 1 × 1 + 5 × 1 × 0.01 + 10 × 1 × 0.0001 + 10 × 1 × 0.000001 + ...
= 1 + 0.05 + 0.001 + 0.00001 + ...
= 1.05101...
= 1.051, correct up to three places of decimals.
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