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Can you explain “time value of money” and “compound interest” and provide examples of each?
A real simple definition or analogy of present Value would be the "Principal" or "Loan Amount" being lent and the future value as being returning the Principal along with cost of borrowing The (1+i)^n is the interest you earn on present value The (i+i)^-n is the interest you pay on future value The first one is the FVIF or future value of a $1 The second one is the PVIF or present value of a $1 Both these interest factors assume interest is paid annually, if the interest payment is made more often within the payment year then interest factors look this way m is the frequency of interest payment, the higher this frequency the more of interest you pay or earn and you pay or earn the most interest when compounding occurs on each small fraction of time This entails here e is the Euler's e  Thus the interest factors turn to this The preceeding examples only considered a single repayment at future date. Now if you were obliged to make periodic loan repayments say in amount of $1 for n number of periods. Then the present value of all such periodic payment is the "Principal" or amount you borrowed. This is the sum of discounted periodic payments as  if we replace 1/1+i with x then this turns out to be geometric series of the form This simplifies to  replacing (1/1+i) for x we get which is the present value of periodic payment in amount of $1 The future value of periodic payments in amount of $1 can be arrived at multiplying the PVIFA by (1+i)^n giving Once again the interest is compounded per annum and for intra-year compounding you would have to at first find the annual effective yield AEY to use as the effect rate is the PVIFA and FVIFA calculation for continuous compounding All the calculation discussed thus far did not take inflation into consideration, if we were to adjust the amounts for a growth of g% then the present value of a $1 would be as follow Once again you would have to use AEY if compounding frequency of interest is intra-year Now assume that each loan repayment increases or decreases by an extra amount Q per period. To find the present value of series of payments P that increase or decrease per period by an amount Q we would do the following calculations Here and All of these calculations have been available in tadXL add-in for finance and incrementally being offered as JavaScript financial functions library tadJS. Please note that the tad series of the financial functions library for various environments such as Excel, JavaScript, PHP, Ruby, Microsoft.net and others are property of the author writing this post. All of these libraries except one for Excel are available for FREE for public use. And the future value of such payments with increments may be found by multiplying the PV by (1+i)^n as follows Here