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What about when time isn’t given in years?

Here look at calculating simple interest today and the formula for simple interest is interest equals principal times rate times time so we can also write this as i for interest p for principal bar for rate nt for time now interest is the amount of interest earned or paid principal is the amount you either invested in the first place or the amount of loan you took

Out rate is the interest rate as a decimal so if it’s given as a percentage we’re going to need to divide by 100 and time is the time in years let’s look at an example ian is investing four thousand dollars for two years the interest rate is five point five percent how much interest will in earn after two years well i’m going to set up what we know and what we

Need to find out pay the interest how much interest will in earn that is exactly what they’re asking so we don’t know the interest that’s what we have to find out the principal is the amount that ian’s investing so they give that to us it’s four thousand dollars the rate is the interest rate as a decimal so we’re going to have to take that five point five percent

And divide by a hundred if you wanted to punch that into your calculator you can feel free to do that it would be five decimal five divided by 100 and t is the number of years so they tell us it’s two years we’re going to plug that into our formula our first step is always to write out the formula i equals p r t our principal is four thousand our rate is zero

Decimal zero five five and our time is two if we take our calculator and multiply these together we’re going to have four thousand times point zero five five times two and that gives us four hundred and forty because it’s a word problem we’re always going to want to have our therefore statement and we want to answer the question how much interest will be and earn

After two years so therefore and we’ll earn four hundred and forty dollars and interest sometimes we aren’t asked for the interest but we’re actually given it so how would we solve for the other variables well we can set up a triangle that looks similar to this i is at our top that’s interest p for principal r for right and t for time so we know i equals p r t

What if we wanted to solve for p well if we covered up the p here we would be left with i equals or i divided by r times t if we wanted to solve for r let’s just pretend this r is covered up so we would have i divided by p times t and if we wanted to solve for t we could cover that up and we have i / ki times r let’s look at some more examples shirley got a $1,200

Loan for two years she paid $90 in interest what was the interest rate let’s find out what we have and what we need i stands for interest she paid $90 in interest so we have i is naívi p is the principal while the total loan was for 1200 so p equals 1200 r is the interest rate which we don’t know and t is time the loan was for two years so t equals two since we

Want to solve for r we’re going to go back and use our formula r equals i divided by pt so r equals i divided by pt why is 90 p is 1200 and t is 2 1200 times two is 2400 and if i work that at my calculator 90 divided by 2400 i’m going to get zero decimal zero three seven five so zero decimal zero three seven five now that’s the rate as a decimal if we wanted it

As a percent we would just move the decimal place over two spots and that’s going to give us three decimal seven five percent if you wanted you could take that number in your calculator and just go ahead and multiply it by 100 to find three point seven five percent because it’s a word problem i’ll write my therefore statement i’ll answer the question what was the

Interest rate so therefore the interest rate plus three point seven five percent looking at our next example doug made a three-year investment the interest rate was 4.5% after three years he earned six hundred and seventy five dollars in interest how much was his original investment so let’s set up what we have and what we need he made a three-year investment so i

Know my t equals three the interest rate was 4.5% so i’m going to write that as a decimal just have to divide by 100 and after three years we already know that’s rt he earned six hundred and seventy five in interest so we are being asked to find his original investment which is the principal amount if we want to plot find our p value remember our triangle i see our

T we want to find p our equation would be i divided by r times t now plug in what i know y is 675 my r is zero point zero four five and my t is three and i’m going to punch in zero decimal zero four five multiplied by three to give me my denominator which is point one three five and now finally i can punch this in i’m going to have six hundred seventy five divided

By 0.135 it’s going to give me an even 5,000 so i’m going to write my therefore statement making sure i’m answering the question the question was how much was his original investment so you could say therefore is original investment was five thousand dollars kim got alone for forty seven hundred dollars to buy a used car the interest rate was seven point five

Percent she paid one thousand fifty seven fifty and interest how many years did it take her to pay off her loan going to write down what we know and what we need to find out kim got a loan for forty seven hundred that is the principal amount she’ll have to pay off the interest rate was seven point five percent so we’re going to divide that by 100 to get our decimal

She paid one thousand fifty seven fifty in interest 1057 fifteen interest how many years that’s what we have to find out if we draw a lovely triangle i p rt and we want to solve for t this time so if we cover that up we would have i divided by pr so t equals pi over p bar and a sub in what we know i is one thousand fifty seven fifty p is forty seven hundred and

Art is 0.075 i go ahead and multiply 4700 times point zero seven five my new denominator is three hundred and fifty two fifty okay so one last step i’m going to divide 1,050 750 divided by 350 250 gives me three and because it’s a word problem i’m going to write it therefore statement how many years did it take her to pay off her loan therefore it took her three

Years if you have any questions on simple interest please leave them in the comments below and i will try to help you out as best as i can

Transcribed from video

Simple Interest Tutorial By InspireMathTutorials