Take $7000 and invest it for 10 years at 5% annual compound interest. How much money will you earn?
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- เผยแพร่เมื่อ 12 มิ.ย. 2024
- How to calculate annual compound interest - algebra word problem exponential functions and compound interest. Learn more math at TCMathAcademy.com/.
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Basic logic; rule 72 for 5%, 72/5=14.4 yrs to double (for 7000 to reach 14000), now $7000 interest take 14 yrs, averaging around $500 /yrs; then 10 year should be around $5000. The closest answer is D $4410
A couple of points. First, you need to explain the difference between compound interest and simple interest. Simple interest - Interest paid at each compounding period doe not stay in the account. Compound interest - interest paid at each compounding period stays in the account and earns interest in future compounding periods. Then you could explain how to do the calculation on paper by multiplying the principal at each compounding period by 1.05 and repeating that 10 times. Then you can explain that the exponential is simply a shorthand way of writing that and that calculators have exponential functions to simplify the arithmetic. The advantage of doing it this way is that the student actually learns what is happening and may understand the process rather than just learning how to plug numbers into a formula. I would also note that exponential functions on a calculator are particularly helpful for fractional exponents which are rather more complicated to figure out on paper. In my view you made a simple problem overly complicated. But who am I to critique your methods, I am just a retired professor with 30+ years of teaching experience.
4402+7000 it's total 11402.
Yes, I got 4.402262387×10³ = $4,402.00 also. That's because Mr. Mathman rounded off his accumulation factor to 1.63 before calculating the amount of interest.
yes because he rounded up 1.62889 to 1.63 which is how you get $8 more.
Not how much do you have.... How much did (your investment) earn.
If he worked for a bank, he would be fired. You are right that you would only earn $4,402.26 dollars. If he paid the customer $4,410 he over paid the customer. When you are dealing with money at a professional level like at a bank, you have to maintain the precision in your calculations to the penny.
Agreed 11,402.26 is correct.
got it by estimation D 350 per year x 10 years has to be a bit more than 3500 thanks for the fun
Did the same!😂
And me😊
compounded
5% of $7000 is $350 .. so 10 years would get you $3500 of interest earned
but that's not one of the answers because that is 'simple interest'.
With 'compound interest' you get interest on the interest
so in year one it's 5% of $7000 and in year two it's 5% of $7350 and so on.
Without working anything out, answers a) and b) are too big and c) is too small
so the answer must be d)
I wish you could have explained where the 1 comes from in (1+.05).
In the real world you are going to be getting your interest calculated yearly - not at the end of the period so the math rules, exponential first would not apply. In actuality the correct answer is $4,402 and change.
Amen. $4402.26
Assuming daily?
Mine is paid monthly at rate/12
@@RustyWalker In that case you are likely getting daily compounding paid monthly. That is pretty much the standard for bank deposits.
the actual "Earning" is $4,402 and NOT the $4,410 that you have stated.
Compound interest is worked out by taking the Log of the interest rate, multiplying by the number of years and then taking the Anti Log of the result.
Subtract 1 and multiply by the amount invested. This gives $4,410 actual earnings.
This is working very well for me. Invested in some stock in 2020 due to the low oil prices during the pandemic. Due to low purchase price, the yield on cost is now just over 64% annually. Paid $5.42 per share. Current dividend is $3.50 annual rate. The dividends received have been saved, then invested in other stocks which pay dividends. Investors refer to this as a dividend snowball, because of compounding, the longer it grows, the faster it grows. The portfolio is currently growing at just over $1000 per month. In two years this will be more then double that. Those who understand this can either pay that 20% credit card debt or take that 5% dividend and compound that for a few years.
The ones that are getting very hurt by this are students with huge loans, and were not taught this. The lenders are getting the compound interest that the students are paying. Pay off the debt as soon as absolutely possible to reduce the amount of that exponential compounding of the interest.
At first I misunderstood the question
and thought investing for 10 years
meant investing 7000 dollar each year
for 10 years.
Simple interest would be 3500 for ten years. Compounding for 10 years would add about 25%. The only answer close to that is D.
Yes, by giving a multiple choice answer it makes it easy to answer. You don't need to look up or know a formula or even work out the answer. It takes away the need to actually do the math!
I used the rule of 72. 5x10=50. So you aren't going to double your money. So d is the only thing close to correct.
No formulas necessary if you look at the choices. Anyone with basic math skills knows that 5% for 10 years has to be more than $3500 due to the nature of compounding so it obviously can’t be options A, B, or C because all those choices are either way too much or less than $3500.
So a simple process of elimination gives you choice D.
Greetings. I am not entirely sure which of the options is correct in that I have not done the calculations. However, the amount earned can be determined by using A=P(1+5/100)^N. That is
A=$7,000.00(1+5/100)^10. The result of this calculation would thereafter be reduced by the initial principal invested to determine the increase, amount earned, over the 10 year period. If the money was invested at simple interest, I would have been able to do the calculations in my head to arrive at $3,500. 00. With compound interest, I will need calculator or pencil and paper, way too many
(1.05)^10.
I got $4402.30, but a quick and dirty calc doing simple interest for 10 years yields answer d). - possible because other answers were not reasonable.
no math is required, a,b, & c, make no sense
D 5% interest for 10 years, is the same as using a .64 simple over the same term... so the GAIN/EARN is going to be .~647 x 7000 = something very close to the answer D
6.3%
I answered the question without calculating. Logic told me it was D . A and B are far too big and C was too small.
Please don't think that you are going to make a real increase in value of $4,410. Because nobody ever talks about inflation. If inflation over this 10 years is 2% per annum (UK government model number) you will only be increasing the value of your investment by 3%. Recently here in the UK Inflation has been 10% and interest 4%. So deposits are losing money at about negative 6%.
At the title card (0:12)), I'm getting close to d) $4400, whic is closest to my actual answer of $4402.262387.
However, I kept the fractional cents rather than rounding to the nearest whole cent.
I want to know where you Bank! I don't know of any bank that rounds off in the favor of the customer. My bank would have kept the $7.74 roundoff error in their pocket. But at least they would be close enough for multiple-choice questions.
they're not rounding up, they're using cd rates where compounding can go 9 digits pased the decial point which pushs the amount up a few bucks, that's also part of the power of compounding!
I also did the math both ways without rounding up, and got 4402. I did it with the power of 10 AND did it year by year.(7000*1.05, then 7350*1.05,....7825*1.05etc. 10 times). I doubt the bank would round up in their calculations.😢
Agree!
Inflation would just eat that up. It would be best you bought something tangible with the money and resell it after 14 years. At least you could keep pace with inflation.
given:
amount = $7K
interest = 5%
duration (n) = 10 years
year one:
A=P×(1+I)
A: amount
P: principal
I: interest
n: # periods
so
A = $7K(1+0.05)
= $7K(1.05)
= $7.35K
year two:
A = $7.35K(1.05)
= $7.7175K
generally:
A = P×(1+I)^n
= $7K(1.05)^10
= $7K(1.629)
= $11.4023K
earnings =
$11.4023K - $7K = $4.4023K
True if you just calculate 1.05^10 to three significant figures (1.629) but using a calculator it is 1.628894627... Hence the difference between $4,023 and $4,402.
If adding the original 7000 total after 10 years is 11402.24
Did you read and understand the word "earn"?
@@typhoon2827 yes, see my 1st comment below
I didn't watch the video, but the answer has to be "D ($4,402)". The rule of 72 says that you will have doubled your money when (years x interest rate = 72). So (10 x 5 = 50), which is less than 72. So, the earnings have to be a bit less than $7,000. If you're taking the SAT, you won't have time to use the formula. You need to fully understand the question, rule out highly unlikely answers, and approximate the math in your head to select the closest answer. It should take 10 seconds, max.
I did this in about 10 seconds. Rule of 72 as you say. 72/5=14. 10 yrs would be 10/14 or 5/7 or about $5000. Closest answer is $4400, so within reasonable estimation.
if the annual rate is 10% on a credit card and the interest is compounded monthly ( this is part of where they screw you) the rate is really 15.2%
Using the formula for compound interest, I get answer A. Annuity = 7000 ( 1 + .05 / 365 ) ^ (365 * 10) were the numbers I used, which is slightly off. The formula is Annuity = Principle ( 1 + (interest as a decimal / interval of compounding) ) Raised to the power of (Interval of compounding * number of years) I think our instructor may have used a monthly rather than daily interval. Time to find out how close I came.
Drat - I forgot about the last part, amount earned, not the total in the account at the end of the time. Answer D is correct. I haven't watched the video yet, but I'm giving myself a wrong answer anyway for lack of care in reading the problem. The formula I used to calculate the total though is correct.
Edit: Another part I missed, annual, so replace 365 with in the numbers I used with 1. I'm currently at 3 minutes in to the video. Let this be a lesson, read carefully.
I got about 1.649 from (e^0.05)^10 instead of 1.63 resulting in making about $100 more. Presumably a compounding interval factor not covered here?
Correct. This was compounded annually. Compounded continuously is where you use e. Otherwise the formula is P*(1+r/n)^nt where r is rate in decimal, n is compound periods per year, and t is time in years.
As 1.05^10 is not an exact number using 5 decimal places gives 7,000 x 1.62889 = 11,402.23. So 11,410 is incorrect. You need to state that the answer should be to 2 decimal places or nearest whole number. Bankers tend not to want pay out nearly $8 more on this investment than they need to :). Also while Maths teachers want to encourage their students to get as a high a mark per test/exam as possible, I disapprove of multiple choice questions to start with and really disapprove of teachers encouraging guessing. How will you know high good a particular student's capabilities are if it is covered by lucky guessing? The only time I have ever encountered any worthwhile multiple choice questions was in the computer marked science assignments during my Open University studies back in 1995-2000. There you had normally some 10 -12 answers each slightly varying from the others in terms of descriptive text and usually including at least one answer totally unconnected to the rest. You really had to know your stuff in order to work out which answer was correct. No luck guessing here!
Agree completely with your comments regarding multiple choice questions and guessing. This guy seems to be a mediocre (and maybe that’s a generous assessment) math teacher. My takeaway from his videos that I’ve watched is that he cares only about views and likes, and cares very little about teaching math.
@@kevinwesterlund1495 Many teachers only want to get their students to pass tests/exams
How would u solve the exponent problem without a calculator because we have to do the problems without a calculator
Simply use the rule 1% compound for 70 years doubles. For 5% the doubling period is 14 years. Simply pick the value closest to 2/3 the initial amount.
50 years ago a banker could solve this without a calculator , he’d look up the factor he needed in an interest table.
Simple. Multiply $7,000 by 1.05 to get balance at the end of year one. Repeat that using the new balance nine times to get to ear 10.
Year 1 - $7,000 x 1.05 = $7,350
Year 2 - $7,350 x 1.05 = $7,717.50
Year 3 - $7,717.50 x 1.05 = $8,103.375
and so on until year 10. Note that in the banking world your bank would likely round the $8,103.375 to $8,103.38 using standard rounding rules. So if you want your result to reflect what your bank statement would show, you need to use the same rounding rules the bank uses. However, mathematically rounding is an error so keep all the decimals to get the correct final answer.
@@todddunn945
Excel is designed for accounts.
D = 11404 - 7000.
Very complicated explanation, which doesn't explain much to many people, I'm afraid.
Simple table with example would be much more usefull.
However I wonder ... how is the student expected to find right answer?
Could he use Excel? Calculator? Pencil and paper?
What’s your justification for rounding 1.05^10 to two decimal places? This results in an answer that is off by about eight dollars.
Also, at about the 12 minute mark, you state that “A is the amount we’re going to make.” That’s incorrect. A is the future value of the investment. The amount that will be made is A-P. Perhaps you should have stated the equation in the more traditional manner:
FV = PV * (1+r)^t, where FV denotes future value and PV denotes present value. Then you might not have gotten so confused and made such a silly mistake. Hilarious that you make a point of saying that 11,410 is incorrect, then you make the same mistake when describing the variables in the equation.
Using the rule of 72, 72/5=15 so it will take 15 years to double your money. This rules out a) and b) Answer c) seems too low. Answer d) 7,0008(1.05)^10-7000 is the earnings.
Rule of 72s tells you your money will double in approximately 72/5 or 14.4 years. So a and b are way too much. Would take 20 years + or -. C is too small even for simple interest paid at conclusion. D is the only answer that will work.
18 minutes with too much talking. Just giving the formula would have been a lot better
7000 * 1.05^10. = 11402.26
Could have done this video in less then 5min. You like to hear yourself talk
$4,402.26.
Some people are misinterpreting the question. The question was how much did the 7K invested earn! Geez.
D 4,410
1.05 raised to the tenth power does not =1.63 It equals 1.628894662677744000. So your answer if off by $ 7.74,. I don't believe a lender will not give the amount you state.
The answer is: $4402.26c.
yeah, 4,402
r in this calculation formual is APR, not interest rate.
You can roughly interpolate in your head using the 7-10 rule. Seven years at 10 percent you double your money and vice versa. Thus the 4400 dollars was the closet for 10-5.
So (1.05)^10 is 1.63
Really !! Should be at least 1.6289 for 5 sig figures.
No bank is going to be this rough, especially not too high.
I believe Einstein called compound interest The eighth wonder of the world
11402
C Or even less after taxes
the correct answer is not listed among the options. The amount earned is approximately $4,380.27
D
Well I know the answer is Not a ,.b and not c I haven’t even really done the problem .I have money invested in various stocks and bonds With various amounts of money invested I also figure out the rate of inflation the value or projected purchasing power of money in the future My point of this you may have more money in the future but it won’t have the same purchasing power even though you put money into account and is made more money it won’t be enough That money even though is more lost value because of inflation
1.05^10*$7000=$11,402.26
yes i did the same. took like 15 seconds with a simple calculator.
I got $4,402.24 earned.
interest x 1.26 x years.
$4410.00
No its not familliar tome but i completed College algebra
Very bad sound system
Minus taxes
Try investing in crypto pump the shib 🎉🎉🎉 or splash it around some good blue chips you can make way more then 4k in 10 years ❤❤
Your math would seem to be flawed. Banks never pay more than they need to....
not a thing
None of the above. You didn’t account for inflation.
You didn't earn nothing because prices went up way more than 5%
Non of these answers are correct. The answer is $4,402.26
i make more money the way he does it. The bank won't pay. If i were a student there is not a correct answer. i hope that is allowed.
Too much talking. Do the problem
My teacher would have used A=7000(1+0.05)^10. We would then use the calculator to find the amount. Interest would be Amount - 7000. How long do you think this would have taken us. You just wasting everyone time. Some screws are loose in your head. You should teach English because you know no maths
My high school math teacher explained this on a blackboard in about five minutes. This guy takes blather and self-promotion to a new level. Blah!
But Mister TH-cam Math Man, I got $3500! That answer isn't one of the choices. So maybe the answer is e) None of the above?
Oh my gosh you talk a lot and that’s a big negative!
The question asks how much do you earn. My salary has f.all to do with you. Do I ask you how much you earn making these videos. Get a real job.
4402.26
D
4402.26
D