Percentage problems

If a loan is repaid in equal monthly payments, first find the interest I, then divide the total C + I by the number of months: monthly payment = (C + I) / (12n). In compound interest, shorter periods raise the number of periods kn while the rate per period drops to r/k; for example 2.5 years with monthly compounding gives kn = 12 · 2.5 = 30. If the final balance A is known, the initial amount is C = A / (1 + r/100)ⁿ. Property such as equipment, furniture or computers wears out and loses value: with depreciation rate r, the value after n years is A = C · (1 − r/100)ⁿ, i.e. each year the value drops by r% of its current value. So the yearly loss gets smaller each year, and the total loss over n years is less than n times the first year’s loss. Banks also use tables for quick calculation: the monthly payment for each 1000 units of loan is read from the table and scaled to the loan.