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let's start out with a single payment compound amount problem first step read the problem closely in this problem we're investing 500 dollars in a savings account with an APR of 6% remember that 6% interest earned annually we're gonna be compounding annually and what we want to know is what the balance will be three years after that initial investment so step number two is to write down what we know and what we don't know in this problem we are given a P of 500 dollars that means an initial investment of $500 we have an AI interest rate of 6% APR and the total period of the investment is three years and remember I is the interest rate per year and n is the number of interest periods what we need to find in this problem is the future value of that account F okay step number three let's draw a cash flow diagram for this problem where we start out with a straight line okay and we are gonna have x 0 no time 1 time-to-time three okay remember that's three years in time at time zero the initial period of the investment we're gonna have a downward arrow that represents our initial investment of $500 remember that means that we have a point of view of the investor in this problem and what we're concerned with is what is the future value of that account how much is it worth three years later we don't know okay to find out that factor that we need to use in this problem an easy way to do that is to simply write what we need to know have / what we do know P I and n that tells us that we need to find F given P and interest rate and a number of interest periods okay remember the also the equation that goes along with f / P is f is equal to P times 1 plus I one plus I to the N okay and for this problem we just simply say $500 times 1 plus 0.06 to the 3 and that gives us a total amount of five hundred and ninety five dollars and 51 cents an alternate way to do the problem and a way to check to see if we got the right answer is to use the factor and remember to use the factor we need to use the prop appropriate notation and that is f is equal to P times factor f / p 6% to the three which is the number of interest periods and that in this problem is 500 times now we need to look up the factor go to our compound interest factor tables scroll through until we get to the 6% interest rate find the factor that we're concerned with in this problem we need to know right here the compound amount factor when we're gift when we need to find F given P scroll down to the number three because you have three interest periods and we're gonna use one point one nine one so let's go back plug in one point one nine one and that gives us an answer of five hundred and ninety five dollars and fifty cents you'll see it's pretty darn close to the first one the one percent are the one cent difference there is due to the rounding in the interest tables so both answers are correct