Annuity mortgage: Duration: 30 years Amount: 485K Interest: 2.06% Gross monthly charge: 1807.25 James decides to take th

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Annuity mortgage:
Duration: 30 years
Amount: 485K
Interest: 2.06%
Gross monthly charge: 1807.25
James decides to take the annuity mortgage(start date: January
1, 2022) . At the start of 2027, just before paying 1807.25, James
makes an extra redemption of 50,000 on the remaining loan (this
redemption does not include interest). The bank will subsequently
handle the remaining loan as a new annuity, and tries to find a
whole number of months remaining, such that the new monthly payment
is as close as possible to 1807.25.
Suppose that the bank will execute this procedure and assume
that the interest rate has remained unchanged since James bought
his house. As compared to the situation without the extra
redemption,
i. How many months will James be finished earlier?
ii. How large is the difference in interest payments received by
the bank?