00:01
So in this problem, we're being asked to complete the table below or complete the table for the unknown quantities and it says to write your complete solutions and answers on one whole sheet of paper so whatever words you're gonna solve this so notice that we're talking about simple interest well, we have a formula to do this to find the simple interest i we multiply the principle by the rate but remember we have to convert our percent to a decimal and times our time but time has to be in terms of years then to find the future value what we do is we take the principle what we start with and we add on our interest so let's start with problem number one where we first need to find the interest so if you have to take our principle, which is for the thousand, we're gonna multiply it by the rate but remember we have to make our percent a decimal to do this we move the decimal point two places to the left so r will be point zero two and the amount of time is three years.
00:49
So we multiply by three so if we take forty thousand times point zero two times three that will give us the interest which is equal to two thousand four hundred so now that's our simple interest and so to find our future value what we're going to do is we're going to take our original which is forty thousand and add the interest which is twenty four hundred well forty thousand plus twenty four hundred is forty two thousand four hundred.
01:14
So that would be the future value so forty two thousand four hundred perfect.
01:20
All right let's take a look at number two where we need to find the principle but we're given the rate in the time as well as the interest so i will be our interest which is twenty five hundred equals our principle which is p times our rate.
01:33
Well, that's ten percent well, so we move the decimal point two places to the left.
01:37
So that'd be point ten times the number of years which is five.
01:41
So now we'll solve for p.
01:43
Well point ten times five is point fifty so to solve for p we need to divide both sides of our equation by point fifty so if we take twenty five hundred and divide it by point fifty that's equal to five thousand so that would be our principle five thousand so now to find our future value, we're gonna take our p value which is five thousand add the interest which was twenty five hundred and five thousand plus twenty five hundred is equal to seventy five hundred so that's how much you would have after five years okay, let's look at number three where we have the principle.
02:20
We need to find the rate we're given the time the simple interest.
02:23
So let's substitute in what we know well, the interest is three thousand six hundred the principle that's p.
02:30
That would be a hundred thousand we don't know the rate, but we know the time is one point five years so to solve for r first, we're going to take a hundred thousand and multiply by one point five, which is one hundred fifty thousand so we have thirty six hundred equals one hundred fifty thousand times r so to solve for r we need to divide both sides of our equation by one hundred fifty thousand so now we'll go ahead and put that in our calculator so thirty six hundred divided by one hundred fifty thousand which is zero point zero two four but remember that's going to be our decimal we need our percent so this time we're gonna move our decimal two places to the right, which means it will be two point four percent so that would be our r value.
03:14
So two point four percent then we can find our future value.
03:18
So to find the future value we're gonna take our starting point, which is one hundred thousand and we're gonna add the interest which was thirty six hundred so our future value will be one hundred three thousand six hundred dollars so we'll add that to our table all right, number four.
03:36
It says that we have we know our principle our rate we don't know the time but we know the interest.
03:41
So again, we're gonna substitute these values into our formula so the interest is fifteen thousand four hundred this is equal to our principle, which is two hundred fifty thousand times our rate, but remember we have to convert that to a decimal so we can move the decimal point two places to the left so that will be zero point zero point five zero point zero four five, but we don't know the time so to solve for t first, we're gonna multiply two hundred fifty thousand by zero point zero four five which will equal to eleven thousand two hundred fifty eleven two five zero times t...