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Does the day of the week depend on the amount of snow, or does the amount of snow depend on which day of the week it is?
What do you think the answer is?
Or, asked a different way, if you were going to graph this, with amount of snow on one axis, and the day of the week the other, would you make the day of the week be the x-axis, or the amount of snow?
i think it is D
Let's try to understand the concept first, and worry about which answer it is second...
well @rainbow_rocks03 asked me what i think it is and so i said D
I will ask a friend to help you cause I can't sorry
Okay, why do you think that? Isn't a key to answering this going to be understanding how to identify the independent variable and the dependent variable?
Which can be deliberately selected and which will be unknown until it is measured?
i thought is was D because you can't control the amount of snow that comes but you can control the time of day you do it at.
so the time of day is the independent variable...and the snowfall amount is the dependent variable because it depends on the time of day...
or as tkhunny put it, you can select the time of day, so it is the independent variable, and you then measure the snowfall, so it is the dependent variable.
can you help with another?
Only one way to find out :-)
What is the final balance for the investment? $20,000 for 3 years at 5% compounded annually $ ___________
do you know the difference between compound and simple interest?
okay, that's a pretty important thing to understand! Simple interest is computed by taking the principal value (the amount you borrowed or invested), and multiplying it by an interest rate. That gives you the interest for one period. If there are multiple periods, you multiply the interest by the number of periods to get the total interest. An example: I lend you $100 for a year, and charge you 5% interest per year. At the end of 1 year, you owe me the original $100, plus 5% interest on $100, which is 0.05*$100 = $5, for a grand total of $105. If we had an agreement that you could borrow the money for 3 years, still at 5% simple interest each year, each year, the balance would go up by 5% of $100. At the end of 3 years, you would owe me $100 + $5 + $5 + $5 = $115 Does that make sense?
yes that makes since
so how do i find the answer to this question?
Now compound interest is different. Notice that the amount of interest added each period was the same with simple interest — just the percentage times the principal value. With compound interest, the interest is computed by multiplying the entire balance by the percentage. For the first period, the result is the same. For the second period, instead of multiplying the principal balance by the interest rate, we multiply the principal balance + all of the interest owed up to that point. $100 + 5%*$100 = $100+$5 = $105 $105 + 5%*$105 = $105 + $5.25 = $110.25 $110.25 + 5%*$110.25 = $110.25 + $5.51 = $115.76 compare that with simple interest: $100 + 5%*$100 = $100+$5 = $105 $105 + 5%*$100 = $105+$5 = $110 $110 + 5%*$100 = $110+$5 = $115
If the interest rate is large, or there are a large number of periods, or both, the compound interest version turns into a much larger number than the simple interest version! For example, if we said 10% interest, and 7 years: $100 turns into $100+10%*$100*7 = $100 + $70 = $170 Compound interest, same interest rate, same number of years: $100 turns into $100(1.1)^7 = $194.87
The formula for compound interest is \[FV = PV(1+i)^n\]where \(FV\) is the future value, \(PV\) is the present value, \(i\) is the interest rate, expressed as a decimal, and \(n\) is the number of periods. Here for your problem, we have\[PV=$20,000\]and we want to find \(FV\) after 3 years at 5%, compounded annually. How many periods do we have, and what value do we use for \(i\) in that formula?
um..... what do you mean by periods?
periods are the chunks of time over which the compounding is done. If you are compounding annually, the length of a compounding period is 1 year. If you are compounding monthly, the length of a compounding period is 1 month.
ok, so we are doing compound annually.... so the period is 3 years
on the question
there are 3 periods... now the interest rate is 5%, how do you express that as a decimal?
Correct. So you can write out the formula, substituting all the known values?
The formula uses \(n\) as an exponent, and you probably don't know how to typeset things, so just put ^ before the exponent, like 2^3 = \(2^3\)
yes, but can you put the numbers in?
what is FV and PV
PV is the amount of money at the start, and FV is the amount in the future. The final balance in the problem is the FV.
FV=20,000 and PV=3?
no, FV is what we are trying to find. PV is $20,000, i = 0.05, n = 3 so the FV = 20000(1+0.05)^3 which is the same as \[FV = 20000(1+0.05)(1+0.05)(1+0.05) = 20000*(1.05)(1.05)(1.05)\]
is the answer 23152.5
I believe it is, yes :-)