Time payments (1 Viewer)

[purplemoon]

Hey
i was doing this question, saw the solutions, and don't know WHY they worked it out in that manner. Can someone please explain why the interest is to the power of both 12 and 18 in the second year ? (might be long, but please bear with me ?):

Jacqui borrowed $400 000 from bank on 1st January 1998. She was not charged interest for the first 6 months. Thereafter, she was charged interest at 15% pa compounded monthly. She agreed to repay the loan in equal installments of M, annually every 31st of December.Her loan is to be repayed at the end of 2001.

QUESTION: how much did she owe on December 31 1999 after making her second payment ?

ANSWER: 400 000(1.0125)^18 -M(1+1.0125^12)

help is greatly greatly appreciated !

thanks

 

[pdang]

2 years (ie 24 months) have passed since she made the loan
interest is not charged on the first 6 months, so is charged on 24-6=18 months which explains the positive term
each repayment is made at the end of the year and the loan was made at the start of the year so the first repayment occurred a whole year after the loan was taken
this is one year (ie 12months) before the day we are considering so this accounts for the negative term