In this last section, we're going to look at interest, and we have one formula to use, the formula for simple interest;
and it says that interest is equal to principal times rate times time. The rate is given as a percent; time is given in years.
So, simple interest, the amount of interest that you'll earn in an account in one year, or any amount of time,
where the interest is earning at a rate that's simple interest, we have I = P(R)(T).
Let's go to the board now and work some problems: "A man invests $2,000 in a savings plan that pays 8% per year.
How much money will be in the account at the end of 1 year?" So, I have this: I = P(R)(T).
So the amount of interest in the account will be the principal, that's $2,000, times the rate, which will be 8%,
so, I'm going to change to a decimal, times the amount of time, which in this case is 1 year.
Now, when I multiply 0.08(2,000) = 160. So, $160 is the amount of interest that's earned in 1 year.
So, at the end of 1 year, the account has in it $2,000 + $160, and that adds up to $2,160.
So, the amount of money in the account at the end of 1 year will be $2,160 dollars because the account earns 8% simple interest in 1 year;
so, principal times rate times time gives me the amount of money in interest that's earned in that account in 1 year.
I add that into the account, and I get the total amount of money in the account at the end of 1 year.
Here's another problem. Problem two: "If $400 is borrowed at a rate of 12% for 1 year, how much is the interest?"
So, again, this is a simple interest problem, and I have interest is equal to principal times rate times time.
So, even though this time we're borrowing money, it's the same formula in simple interest. The principal is the total amount of money;
the rate, in this case, is 12%, so, 0.12; and then, the amount of time again is 1 year.
So, if I multiply 400(0.12)(1), I end up with $48. And this time, we're asked for simply, how much is the interest.
And so, the interest is $48. So, principal times rate times time: the principal's the amount of money that you start with;
the interest rate is a percent, which I changed to a decimal; and then, the amount of time is always given in years.
So, if you borrow $400 at a simple interest rate of 12%, after 1 year, you will owe, in interest, $48.
Here's another problem. Problem 3: "A loan of $1,200 at 9% simple interest is paid off in 90 days.
What is the interest?" So, this time, I have the amount of time given in days. And so, I'm going to have to convert that into years.
So, again interest is principal times rate times time; and time is given in one year. So, I want to find out the amount of interest.
So, I take my principal, 1,200(0.09) so, I write my 9% as a decimal 0.09, and now, I have 90 days.
So, I'm going to write that as a fraction of a year. 90 over, now you might think it should be 365; but when it comes to interest problems,
the standard number of days in a year that we use is 360. That might seem a little odd, but that's the way it is.
And we have to use 360 in a problem like this. So, 90 ÷ 360, not 90 ÷ 365.
Now, I'm going to do this multiplication: 1,200(0.09)(90/360). When I work all that out on the calculator,
I end up with $27. So, $27 is the amount of interest that you will owe if you take out a loan of (12%)
a loan of $1,200 at 9% simple interest and you keep it for 90 days. So, if it's all paid back in 90 days, and it's just simple interest,
the amount of interest that you will owe will be the $27. Let's look at our next problem. Okay, problem 4, let's see:
"A woman puts $5,000 into a savings account that pays 6% annually. How much money is in the account at the end of 2 years?"
Okay, so now, this pays 6% simple interest annually. So, at the end of 1 year, I'm going to get 6% of this amount right here.
So, the first thing I want to do is find out what that is.
So, the interest at the end of the first year will be the principal, the amount I started with at the beginning of the year, times 0.06 times 1 year.
Now, that will come out to be 5,000(0.06); that will be $300 in interest. Now, that's the first year. Now, starting the second year,
the interest is going to be the principal, which is the amount of money that was in the account at the end of the first year,
plus the interest that was earned after 1 year, so, now that's $5,300 times 0.06 times 1 year. So, this time now, I have 0.06(5,300)
that comes out to be, let's see, 6(3) = 18. So, I'm going to have $318.
So, now I want to find the total amount of money in the account at the end of this 2 years.
So, at the end of the first year, I have $300 that I earned in interest, so the amount in the account was $5,300.
Now, I earned another $318 in interest, so I have to add that on to the amount that I had at the beginning of the year.
So, when I do that, I'm going to end up with a total of $5,300 + $318; so, $5,618,
that will be the amount of money that's in the account at the end of 2 years
if the account has $5,000 in it to begin with and earns 6% simple interest annually.
So, first I calculate the interest at the end of the first year; add that onto the principal; calculate the interest at the end of the second year;
add that on, that's my total amount in the account at the end of 2 years.