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- This topic has 11 replies, 2 voices, and was last updated 6 years ago by John Moffat.

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- July 10, 2016 at 10:06 am #325209
1.What is an effective annual annual rate of interest and what is it’s formula?

2.A bank offers a nominal 4%pa, with interest payable quarterly. what is the effective annual rate of interest?

The answer is 4.06%

July 10, 2016 at 12:32 pm #3252221. This is explained in the free lectures on Interest.

2. 4% per annum = 1% per quarter.

The effective annual rate = 1.01^4 – 1 = 0.0406 or 4.06%

July 18, 2016 at 9:19 am #326782Thanks sir.

I do have watched your lectures twice but still has some difficulties in understanding effective annual annual rate of interest. Could you please briefly in wordings re-explain it?

July 18, 2016 at 9:34 am #326808Because of the compounding of interest, it means that (for example) 1 + the yearly rate = (1 + the monthly rate) ^12

It is to the power 12 because there are 12 ‘lots’ of monthly interest in a year.

July 18, 2016 at 4:25 pm #327228thanks sir

July 18, 2016 at 6:45 pm #327310You are welcome 🙂

August 2, 2016 at 6:44 pm #330921Dear sir,

I do have watched your lectures several time but still has some difficulties in understanding effective annual rate of interest. Briefly could you explain in wordings and give me the formula?Thanks.

August 3, 2016 at 7:39 am #331005I have given the formula in my previous answer on this page and I cannot really add anything to the explanation I wrote.

August 7, 2016 at 5:50 pm #3318451.An investor has the choice between two investments. Investment E offers interest 4% per year compounded semi-annually for a period of 3 years. Investment W offers one interest payment of 20% at the end of it’s four year time.

What is the annually effective interest rate offered?The answer is E 4.04% and W 4.66%

2 A project has an initial outflow of $12,000 followed by 6 equal annual cash flow, commencing in one year time. The payback period is exactly 4 years. The cost of capital is 12% per year.

What is the NPV?

The answer is $333-could you please help me to tackle with these 2 questions; in the book, the workings are a bit complicated to understand.

Thanks.

August 8, 2016 at 8:21 am #3319061. The interest is 4/2 = 2% every six months.

Therefore the annual interest rate = (1.02^2) – 1 = 0.0404 (or 4.04%)If there is interest of 20% over 4 years, then the annual interest rate is given by:

(1+r)^4 = 1.2

Therefore r = (fourth root of 1.2) – 1 = 0.0466 (or 4.66%)2. The can inflow must be 12,000/4 = 3,000 per year for 6 years.

So the NPV = (3,000 x 6 year annuity d.f. at 12%) – 12,000August 23, 2016 at 7:58 am #334650What do you mean by “fourth root of 1.2”?

(How to type that in my calculator)August 24, 2016 at 6:08 am #334821Take the square root twice (or look up in your calculator’s instruction book).

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