A = P(1+i)ⁿ ==> compound interest where P= initial Capital, I =interest in% and n the number of years. A is the total amount collected over n years
A= 500(1.0325)¹² ==> 500(1+0.0325)¹² ==> 500(1+3.25%)¹²
The mistake is:
Either she has a yearly interest of 3.25% & she wrote 12 instead of 3 (years)
OR
She got a quarterly interest of 3.25% and in this case she should have divided 3.25& by 12 (4 quarter a year ==> 12 quarter for 3 years) by keeping as exponent the number 12 (right)
1)Now the Amount of A (as she wrote it) =500(1.0325)¹² = 734
2) If she wrote 12 instead of 3, and after correction A=500(1.0325)³ =550
3) But if she had taken the quarterly interest for a period of 3 years (12 Qrtr)
then A =500[1+(3.25%)/4]¹² = 551
