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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%
1. 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%
Thanks 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?
Because 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.
Dear 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.
I have given the formula in my previous answer on this page and I cannot really add anything to the explanation I wrote.
1.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.
1. 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%) – 12,000What do you mean by “fourth root of 1.2”?
(How to type that in my calculator)
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