Let's say, that we have borrowed a $100,000 for a 5 years, with 6% p.a. interest rate. How can one determine the value of a loan payment, if we are making payments every quarter and at the beginning of the interest period?
I know, that solution has to involve a geometric sequence, but I can't find a way, by which I can create one to solve it.
Outline: From the lender's point of view, they should have a value of $F=\$100000\cdot(1.015)^{20}$ after five years.
Your payments must generate that value. If each payment is $R$, then the total value of all the payments at the end of five years is $R\cdot (1.015)^{20}+R\cdot (1.015)^{19}+\cdots +R\cdot (1.015)^1$.
Thus you need $R$ so that the sum of this finite geometric series is equal to $F$.