A credit K (100'000) is to be repayed within t (5) years, including interest rate p (5.25%), by an constant annual sum b.
My idea was the following: Generally each year K/t $ must be payed back. Additionnal to that, the interest rate on the credit must be payed. In the first year the interested rate must be payed on 100'000$, the second year on 80'000$ (...) and in the end (fift year) on 20'000$
As the ammount payed each month must be constant, i thought that the whole interest rate, that must be payed, can be found out and afterwards distributed to the annual payments. So the whole interest rate to be payed equals p(100'000 + 80'000 + 60'000 (...) + 20'000). The part within the brakets is the sum of the arithmetic series K - (t-1)(K/t). The formula for this sum equals t(K+K/t)/2.
Thus the whole interest rate to be payed is p(t(K+K/t)/2). This must be "distributed" to each annual payment, which is the reason why the whole formula must be divided by t.
To sum up: the formula for b is
K/t + (p(t(K+K/t)/2))/t which is the same as K((t+1)p+2)/2t
Unfortunately i get the wrong results. Anyone an idea why??