00:01
Let's say we want to invest some money and we want to know how much money should we invest to have $50 ,000 in 18 years.
00:10
Let's assume we're starting from zero.
00:12
We have no money right now.
00:13
We want to have 50 ,018 years.
00:16
We have an interest rate of 4 .5 compounded quarterly.
00:20
All right.
00:21
So this word compounded should make you think of the compound interest formula.
00:26
And the compound interest formula is the amount equals the principle.
00:31
Times one plus the rate over the number of compounding periods times that same variable and the compounding periods times time now let's see where all these are now we want $50 ,000 so this is our amount that's the amount that we have we have 18 years so that's our time if it's compounded quarterly you ought to make sure that your n is how many compounding periods per t.
01:02
My t is in years.
01:04
So if this compounded quarterly, there's four quarters in a year, right? so this will be n equals or.
01:14
And then i'm looking for how much to invest.
01:16
So i'm looking for what my principal has to be.
01:18
Remember, your principal is your initial amount.
01:22
So now we can just go and plug all these values in.
01:25
So we're going to have 50 ,000 equals p times, 1 plus 0 .045 you always have to convert your percentage into decimals over 4 and then your exponent is going to be 4 times 18 all right so so now we can solve for p by using the order of operation so first let's take care of everything inside of the parentheses here so if we if we divide 0 .045 by 4 that's that's going to give us 0 .01125, right? and then we can also multiply the four times 18 here on the outside that i'll give us a 72, right? then we can add these in here, 125 to the 72.
02:27
And i'm in the 72 might seem like a big exponent and it is, but we're basically almost raising a number that's equal to one.
02:38
So our number actually isn't that big, but you do need a calculator to be able to do these kind of problems.
02:46
So if i raise this to the 70 second power, i'm going to get approximately 2 .233765 approximately, right? so if i divide both sides by this number, then i'm going to get my principal value, of 22 ,343 .72 .72.
03:14
72 cents equals my principle.
03:17
So this is how much i need to put up front.
03:20
And it's basically going to double almost in 18 years with the quarterly compounding period.
03:31
All right.
03:32
So now let's look at another situation.
03:36
Now we're looking to find the rate.
03:37
So what rate is needed to double a $10 ,000 investment in 70 years if compounded monthly? so once again, we see the word compounding.
03:49
So we're going to use our same equation here that we used earlier...