Question

The following payments are made under an annuity: 12 at the end of the 44th year, 11 at the end of the 55th year, decreasing by 11 each year until nothing is paid. Find the present value if the annual effective rate of interest is 3%.

Answer 1

As the payment on the year 55 is just 11 and it decreases by 11 every year, it means that there are no payments after year 55. So, there are only 2 payments in total, one in year year 44 (of 12) and one in year 55 (of 11).

Year	Amount	Disc. Factor Calc.	Discount Factor	Present Value
44	12.00	=1/1.03^44	0.272371782	3.27
55	11.00	=1/1.03^55	0.196767171	2.16
			Total     =	5.43

The answer is 5.43.

Note: There is a chance that the question was supposed to be "decreasing by 1 each year until nothing is paid", in which case the answer would be very different. Please confirm. If the questions needs to be changed, I will rework the answer.

Note: I have not rounded up the discount factors. If you are taught to round it up to some 4 or 5 or such other decimals, please mention that too in the comments, and I can rework accordingly.