A man borrows a sum of money from a building society and agrees to pay the loan (plus interest) over a period of years. If $A is the sum borrowed and r% the yearly rate of interest charged it can be proved that the amount of each annual installment which will extinguish the loan in n years is given by the formula
Find in its simplest form the ratio . Show that this ratio is always greater than and, if r=6.5, find the least integral number of years for which the ratio is greater than .
In the ratio
Is this the ratio in its simplest form?
And how do I show that it is always more than ?