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

where

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

?

Thanks