Question reads: Calculate the pv, at i=3% pa effective, of an annuity where 10 is paid at the end of the first year, 12 is paid at the end of the second year, 14 at the end of third and so on, with payments increasing by 2 pa until the payment series ends at time 20. Solution: PV=8 X An + 2 X IAn, where n = 20. I used the same formula but n = 19, I did this because the payment is made at the end of the period, so if the payments end at t=20, the payment at end of year 20 would not be made. Is it an ambiguous question and if so would I get full marks for using correct formula...Or am I reading it wrong? Thanks for any help Nik
There are 20 years worth of payments made at the end of each year and not 19.You don't have to deduct a year. So that's 10 at the end of the 1st year, 12 at then end of second year and so on.There are still 20 payments being made. the last payment at the end of the 20th year will be 10+2(19)=48.Draw yourself a time line, you will find it easier to understand Kind regards Sanjay
Thank you for your reply. I do get that there are 20 payments made, if you end the annuity at the end of the year, but the question says 'payment series ends at time 20', from this I would deduce it ends at the the start of year 20, hence being 19 payments. Nik
The definition of an annuity in arrears is the present value of 1 payable at the end of n yrs. We are not considering the no of payments, but rather the no of years required to make these payments, which is 20 years. Think of it this way-If I borrowed $12 on New Years Eve and agree to pay $1 at the end of every year then the last payment is clearly on Dec 2025 (2013+12). So 'n' here is 12 years.The same thing is applicable to your question as well. Hope this helps!
Just to be clear - "time 20" is the end of the 20th year. The first year runs from time 0 to time 1, the second year from time 1 to time 2. The 20th year runs from time 19 to time 20. Any payments made in arrears for the 20th year would be made at time 20.
