Description

TenMarks teaches you how to find the relation between principal, rate and time from the simple interest formula.

Transcript

Principal, Rate, Time Now let’s learn about the relationship between principal, rate and time and the problem says that Jimmy deposits $6000.00 in an account that earns him an interest of 6%.About how long will it take for his account balance to reach $7000.00? So let’s look at what are we given. Well what we’re given is amount of money deposited equals $6000.00. This is the principal, that’s the amount of money. The rate of interest which is R=6% that is given to us and we are given that the account balance should reach $7000.00. So the total amount at the end of the period, total amount A in his balance is $7000.00, that’s all we’re given. We don’t know the, what we don’t know is the time. Time T is what we need to find. So let’s do this. What do we know? We know that the amount, total amount equals the principal plus the interest. What do we know? Total amount of the end is $7000.00, we know the principal that he deposited was $6000.00 plus interest which is I. Subtracting 6000.00 from both sides, I get 1000=interest. All I did was took the left hand side, subtracted 6000 and on the right hand side subtracted 6000 as well. So what do I get? I know that the interest Jimmy earned is $1000.00, so Jimmy earns or Jimmy should earn, needs to earn that had should have earned, that Jim needs to earn $1000.00 in interest to get his account to $7000.00, that we know. So now let’s look at what do we know, we know P=$6000.00, we know interest=$1000, we know the rate of interest=6%, what we don’t know is T, time. The formula that we know we can use is interest I=PxRxT, so what are we given, substituting the values. $1000=P which is $6000xR which is 6% or 6/100xT, this is what we need to determine. So now that we know that, let’s multiply. On the left side we’ve got $1000 on the right hand side we got 6000x6, so $36000xT/100. Now that we have this particular equation, we need to separate T. So leave T on the right hand side and move everything else here. So let’s do this, first let’s solve for this. The left side remains the same. Let’s divide the top and the bottom by 100 which is the GCF of both of these. So 36000 divided by 100 over, not over sign, 100 divided by 100 multiplied by T. All I did was take 36000 and 100 divide them both by there GCF which means $1000=36 followed by 1,0 because 36000 divide by 100 is 360xT. Now that I know that $1000=360xT, let’s take a little bit more space. What I'm going to do is divide by 360 on both sides. Because the goal is to get rid of this T, so if I divide by 360 on both sides, right side I'm left with T and left side, I'm left with 1000/360 which is 2.78, 2.78 years, T is always in years. So the time taken for Jimmy’s account to reach $7000 is 2.78 years or approximately 3 years. He’ll have to leave that money in the account for about 3years. The exact number is 2.78 years. Quickly recapping what we did here, what we did was we were given the principal, we were given the rate, we were given the final amount and T is what we needed to calculate. First we applied the principal that the principal plus the interest earned is the final of the total amount, which meant the interest was $1000. Once I knew the interest we could apply that to interest equals principal times rate times time. Applying it, we got $1000=360xT or T=2.78, remember that T is always in years, which means the total amount of time needed for Jimmy’s account to reach $7000 is 2.78years or approximately three years.