Can $3500 grow into $8,500 in 9 years by investing at a 7% annual compound interest rate?
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- เผยแพร่เมื่อ 11 ม.ค. 2025
- How to calculate compound interest - annual compound interest rate and return on investments. Learn more math at TCMathAcademy.....
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Trying to remember old stuff I come up with this:$6434.60 made up like:
3500x(1+0.07)^9 included compounded interest. Then looks like is No at the question of the video. Why using logs?
The original question was can you grow 3500 to 8500 in 9 years earning 7% interest compounded. The answer is no. To prove it all you had to do is plug in the numbers to the formula and see that it was well less than 8500. Determining how many years it would actually take to grow it to 8500 is a totally different problem. Just my opinion.
Absolutely correct. This is a real problem that I have seen from some of my granddaughters’ math teachers (I’m an old guy); in “word problems” they don’t pose the problem correctly, making it difficult on the student to get to the expected answer. This tends to discourage them because it makes math seem arbitrary and it shouldn’t ever be taught that way.
@@danddb2I totally agree and I am an old guy too.
Yes, he had to add a bonus question so he could use logs and make it more complicated. :(
At my age 87 I had forgotten how to do this as have no neeed to do it but your video reminded me and now I may do this. Such fun.
This is exactly what Excel is designed for: you can vary interest rates, investment, number of years and targets.
Thanks for getting right to the point without dragging it out. Perfect. Good lesson.
.... but your teaching technique, and the formula, made this crystal clear.... thanks!
t = 9, it is given!
No, as presented in the problem statement (also it would be a challenge to find organization to give 7%); however one could do the following.
Initial Investment = $ 3500
Time (period) = 9 years
Monthly Contribution = $15
Compound Annually
This would yield $8,590.65 at end of 9 year period -- it is amazing how monthly contributions can help.
Very handy, from time to time! Thanks for the explanation
I completed how much would earn in 9 years. Since this was a yes or no problem I just noted that it was less than 8500 so my answer was no
Rule of 72. 72 divided by the interest rate tells you how long it takes to double your money. It would take a little more than 10 years to just double your $3500 into $7000.
In this period (9 years) you would need an interest rate of 10.36% to reach $8500
Excellent work, vespa. Here is the formula, which can be calculated easily on a scientific calculator: percent = ([(8500/3500)^(1/9)]-1)*100
Thanks. I knew there's a formula but couldn't remember it
Rule of 72. To double your money, divide the interest rate into 72 and that number is how many years it takes to double your money. At 4% it takes 18 yrs. At 6% it takes 12 years. At 8% it takes 9 years. At 10% it takes 7.2 years. At 18% it takes 4 years. This you will probably not believe but you could get 18% on your money at one time during the 70's! The prime lending rate at one time in the 70s was 20%. I did not have 10 grand to invest in a CD at that time but some older guys at work did. Check inflation figures between 1970 and 79. The inflation compounded for those 10 years was over 103%.
Given the compound interest is A=P(1 + r/n)^(nt)
Where A is 8500, P is 3500, r is 0.07, n is 1, and t is 9.
8500 < 3500(1 + .07/1)^(1*9)
8500 < 6534.61 [false]
Therefore, $3,500 cannot grow into $8,500 in 9 years, given an 7% annual compound interest rate.
Great! Practical 😊
No. But in a real world situation, you would also play around with the compounding period. The interest rate may be 7% but how often do you do the actual compounding calc and receive the interest payment? If the calc is done once a year and this is when you get your payment then you will end up with, approx, $6434. On the other hand, if you do the calc every month, and also get the appropriate payment, you end up with, approx, $6560. So, if you can get the bank to do the compounding monthly you end up $126 better off.
Just for fun, if you compound daily, you end up with ~$6571
Do you expect to be able to walk into a bank and get them to do that???
I doubt there are many banks who don't understand the difference.
@@gavindeane3670 Some banks make it a marketing point that they compound monthly. From looking at my bank statements, I can tell you HSBC & Westpac do. Maybe you need to do some reading of what your bank offers and in turn possibly move to a bank that offers better deals.
@@gavindeane3670 NO It was a simple point about how the compounding period will change the return. I swear, people spend too much time trying to look smart on comments. My sentence literally started with "Just for FUN (emphasis added!)".
@@todd727300 I didn't reply to you.
I used the rule of 72 and answered No within the first 20 seconds
Rule of 72 makes this easy.
72 / 7 is a bit more than 10, so at 7% interest it will take a bit more than 10 years to double your money.
>10 years to get to $7000, so no, you will not have as much as $8500 after 9 years.
I had forgotten the formula.
So, I calculated how much the $3500 would become each year at 7% annual compound interest, for 9 years.
First year- 3500x1.07=3745
Second year-
3745x1.07=4007.15
and so on till the 9th year.
In the 9th year it became $6055.68
So, $3500 invested at 7% annual compound interest does not become $8500 in 9 years.
Same here but I gave up after year one 😂
@
I think it is great if you understood what “compound interest” meant.
I did the first 3 years on a calculator and then I saw a pattern so I realized the answer was NO, but I don't know the formula.
I think all students should learn the financial idiom; The Rule of 72
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Holy crap I never knew that , log =exp whoa
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Rule of thumb 10 years at 7% will double your money.
You also have to adjust to inflation
Thank you
8500/3500=2.4286
1.07^9=1.8385
1.07^14=2.5785
You will get it within
14 years.
8500/3500=2.428571
@richardl6751 thanks for your correction.
I will do again.
The math genius is out again?
no only 250 per year growth even with counpounded growth, it's not ehough time thanks for the fun
log(17/7) / log(1.07) = 13.11 years to happen, so NO.
I spent my life in the world of technical math... I got an F on this one ... I hated finance.... 😂
Ditto, civil engineer/architect and early adapter of computers so I used to program this kind of financial calculations in Lotus123... later Excel. Thinks like calculation of net present value to show better insulation of a building will pay off.
I used the calculator in Nerd wallet ( which I was already aware of). No you can’t.
a = 3500(1.07)⁹
= 3500(1.8385..)
At which point we can stop. The result will be less than 7 grand, so No
($3500 x 1.07) x 1.07) ... =
$3500 x (1.07)^9 < $3500 x (1.84)
$8500 ÷ $3500 > 2
No you cannot grow $3500 into $8500 in 9 years at a 7% annual compound interest rate
No.
No
I just went by 7% of 3500.. then just added up 9 years of that.. to see what I got. And then just added it to the 3500.. but you know more about this than I do Mr math Man
If I'm reading you right, that's simple interest. With compound interest, we start by adding 7% ($245) at the end of the first year to get a new balance of $3,745 but then instead of adding $245 again at year two, we add 7% of the new balance ($262.15) and now have a balance of $4,007.15. And so on.
@dazartingstall6680 okay I wasn't doing it right I didn't know what compound interest meant
@@dazartingstall6680 Try exponents Rate plus1 to the NTh power.
@@darrylguilford4061 Yeah I know. a = p(1 + r/n)^nt. My reply above was about what compound interest is, not how to work the problem.
@@ralphmelvin1046 You could have worked it out one line at a time as it's only 9 of them. Keep adding 7% to the accumulating figure and sum them up
No
No.
No
No
no