PV of a geometric increasing annuity due

[MathandBikes]

Question:

You make investments at the beginning of the year for 30 years starting at $100. Each payment after the first increases by 10 percent every year. Interest is calculated at 12 percent per year. Find the present value of this annuity.

(This is my own question that is similar to a question I saw on ADAPT)

My Solution:

v(Ia)angle30 for a geometric immediate.

100 (1/1.12) ((1-(1.1/1.12)^30)/(.12-.1)) = 1864.17

Is this correct? Thanks.

[DanielMena9]

I would have to say it is not correct?

the solution is

100*[1+(1.1/1.12)+(1.1/1.12)^2+....+(1.1/1.12)^29]

= 100{ [1-(1.1/1.12)^30]/[1-(1.1/1.2)] }

= $2,338.42

similarly,

100* a double dots angle 30 with i'=(.12-.1)/1.1
again = $2338.42

where i' is the real interest rate

[FreeYoMind]

I arrived at the same answer as Daniel. Instead of discounting the annuity you need to bring it forward one period.

[MathandBikes]

Right right, thanks all.

Got my mistake now. I'm not sure why I was discounting the thing. Make the mistakes now I guess! Hopefully they won't happen on test day.