Results 1 to 3 of 3

Math Help - Decreasing annuity

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    20

    Decreasing annuity

    A loan is repaid by means of a decreasing annuity payable annually in arrears for 15 years.
    The instalment at the end of the first year is 4,000 and subsequent instalments are reduced by
    150 each year. The rate of interest used is 12% p.a. effective.
    a) Calculate the original amount of the loan.

    b) Construct the capital/interest schedule for year 6, showing the outstanding capital at the
    beginning and end of the year and the interest and capital components of the instalment.

    c) Immediately after the sixth instalment, the interest rate on the outstanding loan is reduced
    to 8% p.a. effective.
    Calculate the amount of the seventh instalment if subsequent instalments are still to be
    reduced by 150 each year and the loan is to be repaid by the original date (i.e. 15 years from the commencement).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Well, do it!

    You have i = 0 .12, then v = 1/1.12

    This gives: 4000v + (4000 - 150)v^2 + (4000 - 150*2)v^3 + ... + (4000 - 150*14)v^15 as the original value of the loan.

    A little algebra gives:

    4000v + 4000v^2 + 4000v^3 + ... + 4000v^15 - (150*v^2 + 150*2*v^3 + ... + 150*14*v^15)

    Just a hair more algebra helps quite a bit.

    4000v(1 + v + v^2 + ... + v^14) - 150*v^2(1 + 2*v + ... + 14*v^13)

    What say you? Can you add it up from there?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    20
    how about the other parts of the question
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Annuity
    Posted in the Business Math Forum
    Replies: 1
    Last Post: June 9th 2010, 05:27 PM
  2. Annuity
    Posted in the Business Math Forum
    Replies: 2
    Last Post: April 20th 2010, 03:10 AM
  3. Annuity Due
    Posted in the Business Math Forum
    Replies: 4
    Last Post: November 8th 2009, 02:20 PM
  4. Annuity
    Posted in the Business Math Forum
    Replies: 1
    Last Post: September 13th 2009, 11:14 PM
  5. [SOLVED] Decreasing Annuity Problem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: August 3rd 2009, 07:35 AM

Search Tags


/mathhelpforum @mathhelpforum