Simple and compound interest

When money is lent, the borrower returns the loan C and pays an extra interest I; it depends on the loan, the term and the yearly interest rate r (in percent). With simple interest the yearly interest is always computed from the original C: I = C · r · n / 100, where n is the number of years (18 months = 1.5 years). With compound interest the interest earned at the end of each period is added to the balance and the next interest is computed from the new balance; after n years the final balance is A = C · (1 + r/100)ⁿ. If interest is added k times a year (half-yearly k = 2, quarterly k = 4, monthly k = 12), then A = C · (1 + r/(100k))^(kn). The compound interest payment is I = A − C. In one year both methods agree, but for n ≥ 2 compound interest is larger.