Quants TVM doubt

CFA Level I Quant
#1

  1. Jim Franklin recently purchased a home for $300,000 on which he made a down payment of 100,000. He obtained a 30-year mortgage to finance the balance on which he pays a fixed annual rate of 6%. If he makes regular, fixed monthly payments, what loan balance will remain just after the 48th payment. A. $186,109 B. $189,229 C. $192,444. - Ans 189,229

  2. 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- Ans 1338

My query is that in the first question the answer is derived by calculating the PV of future cash flow (n= 312) and in the second answer while calculating the pv at year 6 , the ans is calculated by finding the FV of pv (n= 6 rather than n= 25)

Why is the pv calculated in two different ways ?

#2

In #1, the PV is being taken at time t=4 (48 months); in #2, the PV is being taken at time t=5 (60 months). When they say year 6, they mean months 61 to 72

In #1, the original monthly payment is 1,178.74 and the PV just after the 48th payment is 188,933; in #2, the original monthly payment is 946.60 and the PV after the 60th payment is 180,685.2864 with the revised monthly as 1.330.04.

#3

Got it ! Thank you

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