Share your insights or perspective on the financial matter presented in the input.

Can you explain “time value of money” and “compound interest” and provide examples of each?
The fundamental concept of the time value of money is that money now is worth more than the same amount of money later, because of what you can do with money between now and later. If I gave you a choice between $1000 right now and $1000 in six months, if you had any sense whatsoever you would ask for the money now. That's because, in the six months, you could use the thousand dollars in ways that would improve your net worth between now and six months from now; paying down debt, making investments in your home or business, saving for retirement by investing in interest-bearing instruments like stocks, bonds, mutual funds, etc. There's absolutely no advantage and every disadvantage to waiting 6 months to receive the same amount of money that you could get now. However, if I gave you a choice between $1000 now and $1100 in six months, that might be a harder question; you will get more money later, so the question becomes, how much can you improve your net worth in six months given $1000 now? If it's more than $100, you still want the money now, but if nothing you can do will make more than $100, or if there is a high element of risk to what you can do that will make $100 that might in fact cause you to lose money, then you might take the increased, guaranteed money later. There are two fundamental formulas used to calculate the time value of money; the "future value" and the "present value" formulas. They're basically the same formula, rearranged to solve for different values. The future value formula answers the question, "how much money will I have if I invest a certain amount now, at a given rate of return, for a specified time"?. The formula is FV = PV * (1+R)N, where FV is the future value (how much you'll have later), PV is the present value (how much you'll have now), R is the periodic rate of return (the percentage that your money will grow in each unit period of time, say a month or a year), and N is the number of unit periods of time in the overall time span. Now, you asked what "compounding" is. The theory is very simple; if you put an amount of money (the "principal") into an investment that pays you a rate of return (interest), and don't touch the account (in effect reinvesting the interest you earn in the account back into the same account), then after the first period during which interest is calculated and paid, you'll earn interest on not just the original principal, but the amount of interest already earned. This allows your future value to grow faster than if you were paid "simple interest", where interest is only ever paid on the principal (for instance, if you withdrew the amount of interest you earned each time it was paid). That's accounted for in the future value formula using the exponent term; if you're earning 8% a year on your investment, then after 1 year you'll have 108% of your original investment, then after two years you'll have 1.082 = 116.64% (instead of just 116% which you'd get with simple interest). That .64% advantage to compounding doesn't sound like much of an advantage, but stay tuned; after ten years you'll have 215.89% (instead of 180%) of your original investment, after 20 you'll have 466.10% (instead of 260%) and after 30 your money will have grown by over 1000% as opposed to a measly 340% you'd get with simple interest. The present value formula is based on the same fundamental formula, but it's "solved" for the PV term and assumes you'll know the FV amount. The present value formula answers questions like "how much money would I have to invest now in order to have X dollars at a specific future time?". That formula is PV = FV / (1+R)N where all the terms mean the same thing, except that R in this form is typically called the "discount rate", because its purpose here is to lower (discount) a future amount of money to show what it's worth to you now. Now, the discount rate (or yield rate) used in these calculations isn't always the actual yield rate that the investment promises or has been shown to have over time. Investors will calculate the discount rate for a stock or other investment based on the risks they see in the company's financial numbers or in the market as a whole. The models used by professional investors to quantify risk are rather complex (the people who come up with them for the big investment banks are called "quants", and the typical quant graduates with an advanced math degree and is hired out of college with a six-figure salary), but it's typically enough for the average investor to understand that there is an inherent risk in any investment, and the longer the time period, the higher the chance that something bad will happen that reduces the return on your investment. This is why the 30-year Treasury note carries a higher interest rate than the 10-year T-note, which carries higher interest than the 6-month, 1-year and 5-year T-bills. In most cases, you as an individual investor (or even an institutional investor like a hedge fund manager for an investment bank) cannot control the rate of return on an investment. The actual yield is determined by the market as a whole, in the form of people buying and selling the investments at a price that, coupled with the investment's payouts, determines the yield. The risk/return numbers are instead used to make a "buy/don't buy" decision on a particular investment. If the amount of risk you foresee in an investment would require you to be earning 10% to justify it, but in fact the investment only pays 6%, then don't buy it. If however, you'd be willing to accept 4% on the same investment given your perceived level of risk, then you should buy.