Dear friends, this is the problem I am facing now:
I have to determine the value of j, of a geometric progression that goes like this:
payments: 4 4(1+j) 4(1+j)^2 ....... 4(1+j)^19
Time : 0 1 2 3 ........ 20
where the payment of 4 is made at time 1 and the payment of 4(1+j)^19 is made at time 20. I am given that the periodic interest rate i = 0.03, and I am also given that the present value at time t = 0 is equal to 50.42893222.
This is clearly the present value of geometric annuity immediate, so what I formulated the problem as follows:
50.42893222 = 4* [ 1 - ( (1+j)/(1+i) )^20 ] / i - j
50.42893222 = 4* [ 1 - (1+j)^20 / (1.03)^20 ]/0.03 - j
Obviously, finding j is not straightforward, so I was hoping you guys could show me a trick (maybe using the TI BAII Plus or any other way) to solve for the growth rate.
Thanks, in advance for any guidance and/or help,
Best regards,
Paul
I have to determine the value of j, of a geometric progression that goes like this:
payments: 4 4(1+j) 4(1+j)^2 ....... 4(1+j)^19
Time : 0 1 2 3 ........ 20
where the payment of 4 is made at time 1 and the payment of 4(1+j)^19 is made at time 20. I am given that the periodic interest rate i = 0.03, and I am also given that the present value at time t = 0 is equal to 50.42893222.
This is clearly the present value of geometric annuity immediate, so what I formulated the problem as follows:
50.42893222 = 4* [ 1 - ( (1+j)/(1+i) )^20 ] / i - j
50.42893222 = 4* [ 1 - (1+j)^20 / (1.03)^20 ]/0.03 - j
Obviously, finding j is not straightforward, so I was hoping you guys could show me a trick (maybe using the TI BAII Plus or any other way) to solve for the growth rate.
Thanks, in advance for any guidance and/or help,
Best regards,
Paul
How to solve for growth rate in geometric annuities
