Hi, when a tvm problem gives us a rate (eg. 4% Compounded semi-annually or monthly), are we suppose to convert that to EAR to solve the problem or use the rate/period for the same. I am having a difficulty in figuring out which one to use. I am guessing it would depend on what the question is asking. Would really help if someone could clarify this for me. Thanks a ton.
If the question does not specify converting it, you can just increase n to match the number of periods.
Interest rates are quoted as annual rates. If the compounding is not annual, then they’ll be quoted as annual, _ nominal _ rates: you divide by the number of compounding periods per year to get the periodic (effective) rate. In you example, 4% (per year) would be 2% semiannually or 0.333% monthly.
If for some bizarre reason they wanted to give you an _ effective _ annual rate with other than annual compounding, they would have to state explicitly that it’s an EAR.
I am still not clear. Let me cite an ex. In below question, EAR is used. Why?
An investor wants to set up a scholarship fund where she wishes to award $25000 annually in perpetuity. The first scholarship is to be awarded and paid exactly 4 years from today. The funds will be deposited into an account immediately and will grow at a rate of 4%, compounded semianually, for the foreseeable future. How much money must the investor donate tody to fund the scholarship?
4% compunded semiannually = 2 periods per year, at 2% each period. if it were 4% compounded quarterly you would divide 4% by 4, and multiply the years by 4 as well to get a new n (eg. 5 years would be 1% for 20 periods).
In the formula for the value of a perpetuity – V = P/r – r is the effective rate corresponding to the frequency of the payment. In this problem, as I mentioned above, the 4% given is a _ nominal _, annual rate; you have to convert it to an effective annual rate as the payments are annual. Thus, you use r = 4.04% as the EAR.