hello, welcome. We're going to be discussing finding the compound interest rate  and number of time periods. Now you've noticed how we've worked through the  present value and future value calculations, and we've needed to know the  interest rate and the number of periods of time. So now we're going to solve for  the interest rate and the number of periods of time. So let's go ahead and look at the formula for solving for interest, right? So we're going to have interest equals  equals future value divided by present value. Notice it's isolated in the  parentheses. We need to do that first in the order of operations minus one. So  future value divided by present value is isolated. We figure that first, then we  raise it by the number of times right, one divided by the number of time periods.  Then we're going to subtract it by one, because this is going to come out to be  one point, something, something, something. So we need to subtract away the  one so that we can find out our discount or interest rate. So let's look at example of finding the rate right. Matthew choose purchases $1,000 worth of megastore  shares 10 years ago, right? So he just sold them for $3,248 what monthly  compounded rate of return did he realize on his investment? So over 10 years,  his $1,000 purchase appreciated $3,248 we want to know his compounded rate  of return. So remember from compounding, and the last lesson that, the longer  he leaves that in his return, in the greater is going to compound month over  month over these 10 year over this 10 year period. So let's check it out, right?  So interest equals future value divided by present value, right? Raised one  divided by the number of periods, minus one. So we know future value. We  know present value. So we want to solve for I still, future value is a $3,248 the  present value with his $1,000 investment, right? So we'll bracket that. Okay, so  one divided by 10, because it was 10 years, right? Minus one to give us the  decimal. Okay, so now we'll solve. So we'll solve first raised to the 10th minus  one, our interest rate will be 0.00986534 right? So now we'll look at 12 times the interest rate. So this, this is our interest rate per month. Now there's 12 months  in a year, right? So now we need to multiply this by 12. So we will take 12  months. Okay, 12 months and we're going to multiply that by I. I is 0.0986534  when we multiply . 00986534, by 12, 11.84% this is our compounded rate of  return on the Mega store shares over 10 years, 11.84% pretty simple  calculation. So we just have to make sure that we raise one to the 10th. That's  important before we solve that, you'll just divide one divided by 10. That will give you your number, your figure, then you just raise it to that figure, solving for  number of time periods. So let's check this example out. Suppose you want to  buy a new house. You currently have $15,000 and you figure you need to have  10% down plus an additional 5% of the loan amount for closing costs. Assume  the type of house you want to buy is $150,000 and you can earn 7.5% per year  on an investment. How long will it take you to have enough money for the down  payment and the closing costs. So let's look so how much do we need to have in the future? Okay, we need a 10% down payment. Okay, let's look at the down 

payment. We need 10% down payment of $150,000 home times 10% equals  $15,000 okay, now our closing costs, you know, we know that they're going to  be 5% of the sale value, right, minus the $15,000 down payment. So let's look at the closing costs. Okay, so .05 we know we need 5% closing costs, that the  closing costs are going to be 5% of the $150,000 value of the home, right?  150,000 minus the $15,000 initial investment or the down payment. So after we  calculate this, remember the parentheses, order of operations first. So we'll do  the 150 minus the 15. Then we'll multiply it by .05, or 5% to give us 6750, okay,  now our total need now is 15,000 plus 6750 equals 21,750, okay, so now we  need for our down payment and our closing cost coverage. We need 21,7 50.  How are we going to get that? We know that we have an opportunity for an  investment at 7.5% so how long will it take us to accumulate $21,750 at a 7.5%  rate? Now the calculation that you're going to see on your screen is a Excel  calculation. It's very easy. You have to follow, if you follow this formula in an  Excel spreadsheet, you will get this very easy calculation. So let's run through it  real quick so we know that our present value is going our present value need is  15,000 Okay, our future value, we need to raise the closing cost too, right? So  our future value, 6750, I'm sorry. I'm sorry. 21 I messed up on that 21,750, so we need to add the closing costs here, so our interest 7.5% so now, if we were to  run this through our Excel spreadsheet, we would make sure that we put In  present value as a negative number. Present value on any financial calculator  Excel spreadsheet, present value is always has to be put in as a negative  number. Again, our future value, 21, 750, we'll put this in notice the formula is  NPR, and then you'll have the parentheses. So we want to know the number of  periods. So NPR in an Excel spreadsheet formula, if you just type in equals  NPR, you'll see that it'll come up and it'll say number of periods. You'll click on  that, and then you'll input the . 075, for your interest rate. Then you'll input zero  for the payment, because you're not receiving any payments. It's not a bond  purchase. We're not receiving a coupon payment, okay, minus 15,000 for our  present value. And then we'll include the 21,750 future value. So the number of  periods that we are going to need to accumulate the $21,750 is 5.14 years.  That's at 7.5% rate of return. Now, obviously, if we can find an instrument or  security or any kind of asset that will return greater than 7.5% obviously the time to receive the 21,750 will decrease. So the greater return, the more money we  can make, the less time it will take to get the $21,750 



Last modified: Wednesday, February 12, 2025, 11:04 AM