A NOK 5 million, fully amortizing, constant payment mortgage (CPM) loan at 4% interest was granted 10 years ago. The loan has another 10 years until maturity. Payments of interest and principal are scheduled monthly in accordance with terms of an ordinary annuity.

Because of falling interest rates lately, Sunny Bank is now offering to refinance the loan at terms identical to those of the initial (current) loan, except for a lower interest rate of 3% per year and a term to maturity of 10 years.

Refinancing requires up-front payments as follows by the borrower:

1. (1) 2.0% initiation fee payable at closing of the new loan

2. (2) 2.0% prepayment fee charged on balance of current loan

3. (3) NOK 20,000 administrative fee payable at initiation

The borrower has a long-term savings agreement running with the Cool Bank guaranteeing him a 2.5% nominal rate of interest rate per year. If refinancing is chosen, the up-front payments above are paid for by drawing down the balance on the savings account.

(a) Calculate the size of the administrative fee that will make borrower indifferent between refinancing and keeping the current loan.

NB: It would be great if you could show how to solve this by hand using formulas, not only with financial functions on the calculator/Excel.