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).
Mar 12th 2010, 01:45 PM
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.