Thanks AIK. Please also check out www.SimpliTaught.com. I have created this website (it’s free!), with lots of textbook-specific content.

Good question. So that depends on whether the cash flows are semi-annual or not. If you are receiving the cash flows semi-annually as well, then nothing changes - you would discount semi-annual cash flows at the semi-annual rate. For instance, if the question says "you will receive $500 every 6 months, and the annual interest rate is 6% compounded semi-annually.." then you would discount the $500s at 6%/2 = 3%, which is the semi-annual rate, and that's it. On the other hand, if cash flows are ANNUAL, and the APR is 6% compounded semi-annually, then you would first need to convert your APR (6%) into an EFFECTIVE ANNUAL RATE (EAR). I have a separate videos on how to do that. This number will be greater than 6%, and you will use this number to do your discounting. Hope this helps my friend.

JOHAAN THOMAS if an annuity due is deferred, then you will need to discount it back by T years, not T-1, as is the case with the “ordinary” deferred annuity. Thanks for pointing it out; I’ll try to make a supporting video to illustrate this point. Cheers!

Hi Kaur - That's a great question. The key is to make sure that the timing of the cash flows and the interest rate are consistent with each other. In other words, annual cash flows need to discounted at the EFFECTIVE annual rate, semi-annual cash flows need to be discounted at the EFFECTIVE semi-annual rate, and so on. Let me give you 2 examples: Example 1: Let's suppose you will receive $100 every YEAR for the next 5 years (so 5-year annuity, annual cash flows), and the interest rate (APR = 6%) COMPOUNDED SEMI-ANNUALLY. In this case, when you wait one year for the first $100 to come in, you are not just losing 6%/12 = 0.5% every month. Rather, you are also losing interest on that interest income (compounding effect). So, technically, as you are waiting one year for $100 to come in, EFFECTIVELY you are losing MORE THAN 5%. To determine the appropriate rate, you need to figure out your EFFECTIVE ANNUAL RATE, which is (1+6%/12)^12 - 1 = 6.1678%. So you will calculate the PV of this $100 annuity using 6.1678% as your discount rate. Example 2: Same as above, except that you will receive $100 every 6 months for the next 5 years; interest rate is still 6%, compounded monthly. In this case, you need to figure out the EFFECTIVE SEMI-ANNUAL RATE that is consistent with the SEMI-ANNUAL cash flows. And the key, again, is to realize that as you wait 6 months for the first $100, you are not JUST losing 3% interest rate (6%/2); rather, because interest is compounding MONTHLY, you are losing MORE than 3%. How much, exactly? You do the same thing as in Example 1 above, but now only compound the monthly rate SIX times - meaning EFFECTIVE SEMI-ANNUAL RATE = (1+6%/12)^6 - 1 = 3.0378%. The KEY is to make sure that the timing of the cash flows is ALIGNED with the appropriate EFFECTIVE RATE. I am glad you asked this question. I'll make a separate video on this too. But hope this illustration helps!

If I understand your question correctly, then yes, you’re right.

Hey Lee. Sorry for the delayed response. This is a tricky one, since payments are monthly and compounding is quarterly. Rather hard/time consuming to explain in writing. But I'll try to make a video on this separately.

No, not to my knowledge.

Hi Jaelu - Sure. In this example, C = 500, r = 0.04, and T = 7. So, PV = 500 x ( [1 - (1/(1.04)^7] )/(0.04). 1.04^7 solves to 1.3159, and 1/1.3159 = 0.759918. So, PV = [500 x ( 1- 0.759918) ] / (0.04) --> PV = 500 x (0.240082/0.04) --> This math should give you $3001.02.

@@professorikram I get it now, thanks!