Both from the same hf company, but different interviewer.(1) why money has time value?(2) Given a container with 100 base balls, each time you randomly selected one ball, marked it, and returned to the container. If the ball has been marked already, you put it back immediately. Every time before drawing, the container was shuffled. What is the expected number of drawings to have all balls marked? If the result is a series summation type, how to approximately calculate it? What is the error for your approximation?

The second question is a standard expectations calculation: Let Ei be the expected number of balls drawn after the (i-1)th until we get the next unmarked one. Then Ei = 100/(101-i). Summation is 100 times the harmonic series truncated at some point.The first one is interesting. Beyond the simple psychological explanation ($1 now is better than $1 next year), I guess one could also make an arbitrage argument. It might be circular though: you can earn interest because there is a time value of money, so that can't be why there is such value.

Regarding question 1) it's like asking "Why does it usually cost more to book a tennis court for 2 hours than to book it for one hour?" If you receive 1 dollar a year from now, then you have 1 year less (during your entire lifetime) in which you can use the dollar.

I think the answer question one relates to a risk-free interest rate. If the risk-free rate is zero, then money has no time value. A dollar today is equal to a dollar a year from now. If the risk free interest rate is greater than zero (which is generally the case, except sometimes in Japan) a dollar today is worth more than a dollar a year from now - hence it was time value.That's how I would answer the question.

QuoteOriginally posted by: gtoutkastI think the answer question one relates to a risk-free interest rate. If the risk-free rate is zero, then money has no time value. A dollar today is equal to a dollar a year from now. If the risk free interest rate is greater than zero (which is generally the case, except sometimes in Japan) a dollar today is worth more than a dollar a year from now - hence it was time value.That's how I would answer the question.Please reread tetrabit's post on this thread.

I think we all agree that the time value of money is equivalent to a positive riskless interest rate. Risk free rates are driven by at least two factors: opportunity cost of lending money, and inflation. If you have some money, you might be able to make it grow by investing wisely in the instruments of your choice. It seems facetious to point out that any profit made is dependent on you having the cash to invest. If you lend the money to someone else instead, the profit is unattainable and so money-lenders charge interest. The 'riskless' rate (and hence time value of money) arises as a consequence of 'riskless' borrowers such as the American government. Combine this with the phenomena of inflation: £1 now really does buy you more mars bars than £1 in 10 years time. I think the final cause of inflation is beyond the point of the question?If you cannot reasonably expect to be able to put your cash to profitable use, and expect no signigicant inflation, services such as those provided by retail banks (i.e. keeping your money safe from theft, provision of cashcards, transfer of moneys etc.) would still cost money: the riskless rate should arguably become negative - a rationale that was justified by events in Japan during the late 90's.

Does anyone pay attention to the last part of question (2)? What is the errow incurred in approximating a finite harmonic series by log?

QuoteOriginally posted by: daydayupDoes anyone pay attention to the last part of question (2)? What is the errow incurred in approximating a finite harmonic series by log?Google can answer that one, so where's the fun?

It's true that google can answer this.The answer, of course, depends on 'n' (the number of different baseballs).This problem is essentially identical to the 'coupon collector' problem I just answered.I didn't use the approximations for the harmonic series because my equations editor is being a piece of poo. Check this out, though, as it gives you everything you're looking for:http://en.wikipedia.org/wiki/Coupon_collector's_problem