[volora]

What is the present value of 4 annual payments of $300 each with the first payment being received immediately? Assume you can invest money at a 10% stated rate with semiannual compounding.

My answer 1,063,79, just want to make sure if that's the right answer.

[ROLCAM]

Your answer must be incorrect.
It is too low.
To start with the answer must be over $1,200.
You see $300 four times is $1,200. This is of course without interest.
Now see the calculations and the answer is yours:-

1ST 6 MOS 300.00 315.00
2nd 6 MOS 315.00 330.75
3rd 6 MOS 630.75 662.29
4th 6 MOS 662.29 695.40
5th 6 MOS 995.40 1,045.17
6th 6 MOS 1,045.17 1,097.43
7th 6 MOS 1,397.43 1,467.30
8th 6 MOS 1,467.30 1,540.67

The answer is $ 1,540.67.

[ArcSine]

Rolcam, I initially started down the same road you did, but then I noticed that the 'present value' in this case seems to be from the perspective of the recipient of the payments ("... with the first payment being received immediately... ").

Volora, note that your problem can be viewed as using a 5% discount rate per 6-month period, and that the 4 payments are received at the end of periods 0, 2, 4, and 6 (corresponding to immediate; end of first year; end of second year; end of third year).

Thus, you can price the cash flow stream with



Equivalently, you can first determine the effective annual rate (10% per year, semiann compounding, = 10.25%). Then, price the cash flow stream using the familiar 'PV-of-an-annuity' formula--remembering that the first payment is received immediately, while the remaining three payments form an 'ordinary' annuity:



Same result, whichever method you prefer.