4% compounding quarterly, i.e. 1 % per quarter
\(Q_1\) :1% of 10000 = 100
\(Q_2\) :1% of 10000 + 1% of 100 (interest for\(Q_1\)) = 100 + 1=101
\(Q_3\) :1% of 10000 + 1% of 100 (interest for\(Q_1\)) + 1% of 101 (interest for \(Q_2\)) = 100 + 1 + 1.01 = 102.01
\(Q_4\) :1% of 10000 + 1% of 100 (interest for\(Q_1\)) + 1% of 101 (interest for \(Q_2\)) + 1% of 102.01 (interest for \(Q_3\)) = 100 + 1 + 1.01 + 1.0201 = 103.0301
Total interest = 100 + 101 + 102.01 + 103.0301 = 406.0401
Now using option
Option A: 20001 at 2% semiannually
1%of 20001= 200.01
1%of 20001 + 1%of 200.01 = 200.01 + 2.0001 = 202.0101
Total interest = 200.01 + 202.0101 = 402.0201 which is not equal to 406.0401
Option B: 20101
Using the same pattern total interest is 201.01 + 201.01 + 2.0101 which is not equal to 406.0401
Option C: 20201
Using the same pattern total interest is 202.01 + 202.01 + 2.0201 which is equal to 406.0401
Thus answer is
Option C
_________________
Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com