Perpetuity and annuity problem

[bewger]

Mary deposits 1000 into a fund at the beginning of each year for 10 years. At the end of 15 years, she makes an additional deposit of X.

At the end of 20 years, Mary uses the accumulated balance in the fund to buy a perpetuity-immediate with annual payments of 2000 per year for 10 years, and 1000 per year thereafter.

Interested is at an annual effective rate of 5%. Calculate X.

My problem is the bold statement.

I wrote it as 1000/.05 + 2000(a angle 10)
The solution is 1000/.05 +1000(a angle 10).

Is it because the perpetuity payments start the same time as the annuities payments? Meaning, for the 1st payment, it is 1000(from the perpetuity) + 1000( from the annuity)?

Something like that?

[Gandalf]

Originally Posted by bewger

I wrote it as 1000/.05 + 2000(a angle 10)
The solution is 1000/.05 +1000(a angle 10).

Is it because the perpetuity payments start the same time as the annuities payments? Meaning, for the 1st payment, it is 1000(from the perpetuity) + 1000( from the annuity)?

Something like that?

Yes. Alternatively, you could treat it as a 10 year annuity for 2000 and and a 10-year deferred perpetuity for 1000.