A fund is set up where each member will receive $100. Assume that 10 people will qualify at the end of one year and then 15 at the end of 2 years. [Making this an annuity immediate situation] So, this increase will go on till the number of qualifiers are 50 per annum and will remain constant. Effective interest rate is 0.03.
What is the total sum needed to meet the future obligation ?
The way I think about this is that, you have 500 as your first payment and then using the increasing annuity formula we can know that the payments are also increasing by $500 each year till member total = 50. This also makes it clear that time = 9.
So, to solve this we would set up the equation as 500(Ia)9 + 500(a)9 + v^9 *5000/0.03 The reason we are adding v^9 to this mix is because the intent is to find the future value, making it important to find the present value of 5000 which can be added back to get the FV. (Correct? If not, please explain why).