(a) Show that at an annual rate of r, if interest is compounded n times in a year, then the amount in the account at the end of the year is A(1 + r/n)ⁿ, where A was the amount in the account at the start of the year.

(b) Show that if A₀ is initially invested in an account that pays annual interest r, compounded n times yearly, then the amount in the account after t years is A(t) = A₀(1 + r/n)^nt.