Time value for a sequence of ordinary annuities

CFA Level I Quant
#1

A borrower has entered into a fully amortizing, 4%, 30-year fixed mortgage with monthly payments. The principal is GBP 200,000. At the end of 5 years, the borrower wants to change the payments so that the mortgage will be completely paid off in another 15 years. The adjusted monthly payment (in GBP) needed to pay off the mortgage in the borrower’s time frame (Years 6–20) is closest to:

A. 955
B. 1212
C. 1338

Answer: C. 1338.

Please help me understand how they landed up with that answer. Thanks.

#2

The key is determining the principal balance after 5 years, then using that as the PV for a 15-year loan.

#3

I don’t have my BAII on me, but lemme get ya started:

P/Y 12 C/Y 12 (I am assuming monthly compounding)
END
CLR TVM
360 N 4 I PV 200,000 CPT PMT $x

To get the outstanding principal after 5 years, you can use the AMORT function or just find the PV of the remaining 25 years’ payments.