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Exercise 3 : An amount of $ 500 is invested in an account paying 1.2 % interest compounded annually ( meaning they don't add interest until the end of the year , so the start of the next year you have the money plus interest )

( a ) Please write a recursive definition for P ( n ) , the amount in the account at the beginning of the nth year . Hint P(1) = 500; Forn > 1 , to calculate the amount in the year , you need to use ( 1 + 0.012 ) times the amount in the (n - 1) * thyear

( b ) After how many years will the account balance exceed $ 570 ? ( You can write a c++ program to calculate )