How do you calculate the constant payment by hand ?

It is an armotized loan problem: “A homeowner borrows $ 100,000 on a mortgage loan, and the loan is to be repaid in five equal payments at the end of each of the next 5 years. The lender charges 6 percent on the balance at the beginning of each year.” I know you can use the PMt function on Excel, but how does it do it?

There are some hints in the book but I didn’t get: “You could also factor out the PMT term, find the value of the remaining summation term (it’s 4.212364), and then divide it into the $ 100,000 to find the payment, $ 23,739.64.
Where does 4.212364 come from?

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