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finance - a la shmoop how do you calculate rates of return? well invest a dollar get

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more than a dollar back right? well yeah you hope so anyway in in finance land [dollar bill on table]

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and Wall Street and any other professional gig. well rates of return

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from financial investments are generally stated as annual returns, so calculating

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a rate of return revolves around the one year at a time thing. there are a ton of

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curveballs that get thrown into these calculations. here's a big one,

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dividends. well guess what clueless financial journalists with little to no [dividends defined]

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real schooling in finance quote stock market returns all the time. let's say

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that shares in random example industries traded at the same price at the

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beginning of the 1970s as they did at the end of the decade. prices for random

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example industries were totally flat from 1970 to 1980. that's what one of

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those journalists might say. and they don't even get fired for making such a [man reports news]

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narrow statement .no nothing happened at all. and wrong. had they taken this course

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they'd have realized that monster-sized dividends were paid out during that time

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period. five six seven eight percent a year, each year. yet the journalists

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ignored them when they stated that the stock market was in fact flat for a

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decade and maybe shares of that company were also flat for a decade. but it

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implied that they got no return from their investment which is absolutely [icons of stock market and a stock deflate]

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wrong. did readers get their money back for that bad journalistic work? yeah we

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doubt it - well what about zero coupon bonds? that is their bonds that pay no

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dividends or interest along the way and they sell at a discount to par. what does

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that mean? that is $1,000 par value bond pays you a grand in seven years. well how

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do you calculate the annualized rates of return there? well today that bond sells

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for six hundred forty two dollars. like you buy it today for six hundred forty

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two you get a thousand bucks in seven years. well what's the rate of return on [zero coupon bond rates of return listed]

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that bond? hmm. well vanilla bonds like these we're a whole lot easier to

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calculate. because like you got the interest rate right there on the thingy.

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yeah so the question is really what interest rate will accrue and then

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compound for this bond such that in exactly seven years you get a thousand

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bucks? well if it compounded at ten percent a year the compounding would

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look like this. you see the table right there and whoa we've already passed the

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grand way ahead of seven years. so the compound rate must be less than ten

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percent right well what if it compounded at five percent a year well then the [compound rate listed]

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rates of return would look like this and basically we're just multiplying 1.0

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five times a 6.2 and we take that compound totally multiply 1.05 again and

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so on and so on. much closer .well here's the formula you'll want to remember.

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where f is the face value PV is the present value and n is the number of

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periods. well in our example the face values a thousand bucks, the present

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value is 642 dollars and the number of periods is the number of years or seven

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years. all right well then we just you know put our handy-dandy calculator to [mathematical formula shown]

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work and get a yield of well right around here. so here's the key idea rates

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of return are an annual thing when quoted among finance professionals. among

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fun dance professionals well and maybe a different story. [three stooges pictured]

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