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Write for me capstone student activities unit 4 lesson 22 do my capstone review trs old age problems essays on friendship hi guys this is miss goal today's lesson is module 4 lesson 6 simple interest tasks and Commission real-world problems your outcomes for today's lesson are students solve simple interest problems using the formula I equals P times R times T where I is equal to interest P is equal to principal R is equal to interest rate and T is equal to time when using the formula I equals P times R times T students recognize that units for both interest rate and time must be compatible students convert the units when necessary students solve real-world percent problems involving tax gratuities Commission and fees students solve real-world problems involving percent using equations tables and graphs and finally students identify the constant of proportionality tax rate Commission rate etc in graphs equations tables and in the context of the situation the first thing I'd like you to do is to pause the video and complete the opening exercise when you're ready to continue unpause the video and please check over your answers and please check over your answer so if you notice with each of these examples they actually are all saying the same thing they're asking you to find ten percent of two thousand what's different about them is that they are looking at different real-world scenarios so a is talking about Commission Commission is the amount of money that a person makes when they are working as sales jobs they usually make a percentage of their sales Part B is talking about the taxes that are paid for a hotel room Part C is talking about the shipping fee for shipping a new computer and printer and Part D is talking about the tip on a dinner bill for a wedding rehearsal dinner so we can see the same mathematics applied over several different situations one new formula that we need to look at in this lesson is how does calculate what's called simple interest now simple interest is the idea of your money in a bank account collecting interest but it's always based off of the original amount you put in the bank so simple interest is principal times rate times time and so when we change these into variables we get I equals P times R times T so let's talk about what those different variables mean the principal is the amount of money that you're starting with in the bank account the rate is going to be your interest rate so that is a percentage so you're going to need to turn that into a decimal as we've talked about in this module it's usually based over a period of time typically an interest rate over a year T in this scenario is the time and what you need to understand is that both T and R must be compatible so if they tell you the interest rate is based over a time period of a year but the time period they give you is only six months you're gonna have to turn six months into a year's time so that would be half of a year so you have to always be aware that your rate and time must be compatible using that idea let's take a look at example one can money grow a look at simple interest lira invest $100 in a savings plan the plan pays four and a half percent interest each year on his hundred dollar account balance how much money will Larry earn in interest after three years after five years so we're looking at calculating simple interest so we're starting with our formula I equals P times R times T so the principal is the original amount that was invested in this case $100 so we can fill in P with 100 the rate is the interest rate which is four and a half percent so we're gonna have to turn four and a half percent into a decimal so four and a half is four point five percent and so if we turn that into a decimal we're going to get point zero four five so we'll multiply this times zero point zero four five and the time is first three years now we need to make sure that this matches and it does say that it pays four and a half interest each year and we're eight years so we know they are compatible so we multiply it this one by three and multiply these out and we will get 1350 and this is when our interest rate was over three years and we can also calculate what our interest rate is over five years so our principle is still the same here our interest rate is still the same but this time it's over a course of five years we'll change that to a five and the effect this has is it will be $22.50 how can you find the balance of Larry's account at the end of five years so this is just calculating the interest so we know that interest is then added back into the bank account so here we would take the 2250 that they earned an interest and add it to the principal so we have a final balance in Larry's account of one hundred and twenty two dollars and fifty cents so you always want to be aware of whether they are asking you for the final account balance or just the interests example two time other than one year a one thousand dollar savings bond earned simple interest at the rate of three percent each year the interest is paid at the end of every month how much interest will the bond have earned after three months so in this case we know that the interest rate is 3% per year but we're only looking at how much interest will have been earned after three months so when we're going to calculate this we're still starting with our formula I equals P times R times T the principal in this case was 1,000 and the rate is 3% so we'll turn that into a decimal point zero three however when we're looking at the time we have to translate that into the equivalent of years so when we turn three months into a year we'd want to divide that by 12 and this gives us one quarter of the year so instead of multiplying by three we're gonna multiply by one quarter so you always have to make sure that you are looking at whether the interest rate period matches the time period units multiplying these out we end up with an interest value of seven dollars and fifty cents notice in this question they're not asking for the final amount that was in the savings account so we're just answering how much interest was earned so I stopped at 750 I didn't add it back into the thousand dollars example three solving for P R or T so they won't always give you PRT and ask you to find interest times they're going to give you two of the three elements and then they'll give you the interest and you have to solve for the unknown element just like any other situation we would always use our unknown element as a variable and you can leave it as the variable given or you can always change it to X if you're more comfortable with that so example three says mrs. Williams wants to know how long it will take an investment of $450 to earn $200 in interest if the yearly interest rate is six point five percent paid at the end of each year so let's start with our interest formula I equals P times R times T and let's fill in what we know we know that she wants to earn $200 in interest so we can replace I with 200 the principal is the amount that she invested so this would be $450 the rate for this is six point five percent so as a decimal that would be 0.05 is how long and that's what they want us to calculate how long will it take so we have T and you can either leave it as T I don't really like to use T as a variable so let's change it to X so what we're doing here is just solving an equation we'd start by simplifying this side so we're gonna multiply 450 times point zero six five and when we do that we get 29 25 now if I want to solve for X we're multiplying 29 25 by X so we're gonna do the opposite operation which is to divide those cancel and we get X is equal to six point eight four now because it's paid at the end of each year in order to get to the $200 or more we're going to have to actually go up so we'll round this up to seven years capstone recruitment sydney order New York Conservatory for Dramatic Arts.