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in this video we're going to talk about how to use the simple interest formula to solve word problems so let's start with this problem John invests 5000 in a savings account at an annual interest rate of 7% for five years how much money did he earn in interests so what's the total interest that he received in the course of these five years so the equation that we're going to use is the simple interest formula I is equal to P R T where I is the total interest received which is what we're looking for P is the principal that's how much money he invests in Mika which was 5,000 R is the annual interest rate which is 7% but in a form of a decimal the decimal form of Somerset is seven divided by a hundred which turns out to be point two zero seven and T is the time in years so C is five years so all we gotta do is take 5,000 multiplied by point zero seven times five so he receives a total of 1750 in simple interest now in Part B what is the total value of his savings account at this point so keep in mind he initially put in 5,000 and his account was credited with 1750 and interests so as a total account value at this point is $6,000 and seven excuse me six thousand and seven hundred fifty dollars so that's how much money he has when the account at the end of five years using the simple interest formula so this is the answer for Part B and this is the answer for Part A number two Sally invests eight thousand into an account paying an annual interest rate of eight point seven percent how many years will it take for her to earn four thousand eight hundred seventy two dollars and interests the equation that we need to use once again is I is equal to P R T so the interest that she earned in these years are four thousand eight hundred and seventy two dollars the principal the amount that she puts in the account is eight thousand dollars SP R is the interest rate so if we take eight point seven and divided by 100 R is point zero eight seven that's the decimal equivalent of eight point seven percent our goal is to find T we need to find the value of T in this problem because we're looking for how many years is going to take her to earn this level of interest so the first thing we need to do is multiply eight thousand five point zero eight seven which is six hundred and ninety-six now the next thing we need to do is divide both sides by six 96 so four thousand eight hundred seventy-two divided by six ninety six is seven so therefore it's going to take her seven years to earn four thousand eight hundred seventy two dollars in interests if she invests eight thousand dollars into an account pain and a no interest rate of eight point seven percent number three Mary invests three thousand into a savings account in four years she earns a total of seven hundred sixty eight dollars in interest what is the annual interest rate offered by this account so we're going to use the same formula now in this problem what's I what's P what's our and what's T the three thousand is the amount of money she puts into the savings account so that is the principle the $768 is the interest so we can replace I with that number now we're looking for the annual interest rate so we need to find the value of our is for so first let's multiply three thousand by four that's going to be about twelve thousand now the next thing that we need to do is divide both sides by twelve thousand to isolate R so R is going to be twelve thousand I mean it's going to be seven hundred sixty eight divided by twelve thousand so as a decimal that's three zero six four to convert this into a percentage multiplied by a hundred so the interest rate is about six point four percent so that is the annual interest rate offered by this account number for James invests twenty five thousand into an account paying eight percent annual interest how many years will it take for his account to reach forty-three thousand so the principle is 25 thousand and interest is going to be added to that principle over time and this final account value it's going to be forty-three thousand dollars after a certain time period has elapsed so the interest that he receives during that time is the difference between forty-three thousand and twenty-five thousand so if we subtract those two numbers you should get eighteen thousand so that's how much money he's receiving in interest in its time period and we got to find out what that time period is so our goal is to find seen how many years will it take for his account to reach that level so using this formula is equal to P RT we have the interest earned which is eighteen thousand starting with a principal of 25,000 the annual interest raised eight percent eight divided by 100 is point zero eight so our goal is to find the value of T so first let's multiply 25 thousand by point zero eight so you should get 2,000 and now let's divide both sides by two thousand so 18,000 divided by two thousand we can cancel the three zeroes so it's equivalent to 18 divided by two which is nine so it's going to take in nine years for his account to go from 25,000 to 43,000 if you should receive an 8% in our interest rate so it takes nine years to earn 18,000 in total interest so that's it for this video so now you know how to use the simple interest formula to solve problems like this now I want to show you one of my algebra courses that might be useful to you if you ever need it so go to udemy.com now in the search box just type in algebra and it should come up so it's the one with the image with the black background so if you select that option and if you decide to go to course content you can see what's in this particular course so the first section basic arithmetic for those of you who want to focus on addition subtraction multiplication and division and it has a video quiz at the end it's a multiple choice video quiz you can pause it work on the problems and see the solutions they Club is long division and multiplying two large numbers and things like that the next tutorials on fractions add in subtracting fractions multiplying dividing fractions converting fractions into decimals and so forth so you can also take a look at that next solve the linear equations which we covered and just more examples if you need more help with that the next topic order of operations which is also useful graphing linear equations you need to know how to calculate the slope needs to be familiar with the slope-intercept form standard form and just how to tell if lines are parallel perpendicular and so forth and as a quiz that goes with that as well the next topic is on inequalities and absolute value expressions which are also seen into the goal algebra course and then we have polynomials and that's a long section and then factoring you just that's not the topic you need to master and then system of equations you can solve it by elimination substitution there's also word problems as well sometimes you got to solve equations with three variables XY and Z so that could be helpful next quadratic equations how to use the quadratic formula how to graph them how to convert between standard and vertex form and then you have rational expressions and radical expressions solving radical equations simplifying it things like that and every section has a quiz so you can always review what you've learned if you have a test the next day so here we have complex and magic numbers need to know how to simplify those exponential functions logs I have a lot of videos on logs and then just this is just functions in general the vertical lines has horizontal lines has had itself or functions even or odd and then conic sections graph in circles hyperbolas ellipses parabolas and things like that this two video quizzes because it's actually a long section and finally arithmetic and geometric sequences and series so that's my algebra course if you want to take a look at it and let me know we think