You invested $7000 for 10 years at 5% annual compound interest. How much did you earn?

[@stevemoening2205]

Using a financial calculator the answer is $4,402.26

[@aryusure1943]

@stevemoening As doing it the hard way like I did (year by year). I came up with $4402.76. I must have missed 50 cents along the way. ;)

[@chrisbyrne5678]

That’s what I made it too !! 👍

[@markhurlock3891]

That's the right answer in today's nominal dollars, but accounting for inflation it's maybe 75% of that.

[@margaretmargaret7163]

If you use correct amounts 1.62889463 instead 1.63 it give 11402.2624 it's mean correct answer is 4402.26

[@genelowry5666]

Right, John rounded the interest factor from 1.6288 to 1.63

[@Luis-zu3pb]

Hello Mr. KZbin math man, I am glad to get the formula for this problem. If only the back would round-up as you did. I did get the correct amount by simply multiplying 7000 ×1.05 progressively 10 times, which totaled 11,402.26. With a total earnings of $4,402.26. Almost $8 off your answer. That's ok, I'm still learning from your channel. 😏

[@Workingman-u7s]

Mr. Math Guru rounded up way too early. He fucked it up big time.

[@Poult100]

I'm glad I don't have to do that long-hand anymore! Thanks!

[@rodfulford4306]

I knew there was a formula but forgotten, thanks for reminder. I also used to know how to create it, but also forgotten!

[@Ricky_B4]

I know there is a future compound interest formula but I have forgotten it so I would just multiply 7000 x 5% then at the end of year two it would be 7350 x 5% etc etc til the end of year 10 = 11402.26 - 7000 = 4402.26

[@newsnowriversidesgtrock]

you did it right. The math teacher did it wrong. Your answer is correct he is off by about $8.00.

[@kennethwright870]

Subtract the original $7k to arrive @ what you earned. Best

[@johnopalko5223]

Using the formula, I got $4402.26. Using the "Future Worth of One Dollar with Interest Payable at Beginning of Each Period" table from Jack C. Estes's book, _Compound Interest and Annuity Tables,_ [McGraw-Hill, 1976], I got the same answer. This was using ten decimal places. If I used only four, the answer was $4401.60. Be careful when you round. Try not to round intermediate results. Do all your calculations with as much precision as you can and then round the final result.

[@richardl6751]

“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn't … pays it.” ― Albert Einstein.

[@richardl6751]

As has be said in the comments the answer is off by almost eight dollars. The problem happened with rounding 1.628895 to 1.63. Rounding always introduces errors. With large numbers and long terms the errors increase.

[@Workingman-u7s]

Mr. Math Guru got lazy and he fucked it up.

[@aryusure1943]

@richard Thank you for that precision. I did the problem with lower numbers and came up with the same result with his formula and doing it year by year. But what can be done to avoid errors since the decimal value is infinite?

[@dennismayer4936]

Thanks for the lesson. I didn't realize how many mathematics skills ive forgotten. Im rusty!

[@gregfaris6959]

The answer is correct, but incomplete. A more complete answer would be that the gross earning is $4,410, and the bank or investment firm's fee is $4,411, meaning we lost $1, not counting for the devaluation of that money due to inflation, which at a very ideal 3% annual rate would take away another 1,838. The happy face is for the bank.

[@jai-jaihadley1747]

Ok so perhaps if we all wanted the a+ we might not have got because we wouldn't have known to round at the same point he did but still, the principle is sound and i learned something today. For that I'm thankful to him. Appreciate your work man, thanks

[@ange-bernardferracci4278]

It depends on how the compounding is made the formula is (1+1/n)exp n the limit is number e itsrlf

[@olenfersoi8887]

Not sure why I got slightly different. First year principal & interest is 7000*1.05, each year after is multiplied by 1.05 so the answer is 1.05 to the 10th power x 7000...& I come out qith 4402 m not 4410 Now, having see your work, I realize I am correct, because I did not round down to 1.63

[@leedickie8557]

A great kesson as always but because I didn't set the number of decimal places fro the compound interest I got $11,402.26. Being cynical i could see a bank doing this to pay out less.

[@TerrySmith8]

I'm going to go with your results, since I doubt the bank would round up and end up giving the customer slightly more that 5%.

[@Briarbuddy]

$4402.21

[@panlomito]

This is a perfect problem to solve with Excel... 😊

[@dragoncarver287]

I did it the hard way starting with 7000 and mulitplying by 5% and adding it to the principle. going through it 10 times gave me 11,402.26. Doing it with the formula I came up with the same number. Used the "calculator" that came with Windows. Make sure you do PEMDAS correctly

[@32shada]

Altogether $11,402.46...total interest earned was $4,402.26...principal invested was $7,000.00

[@ExploreWithIsaac]

Your rounding of that number from 1.628 to 1.63 changed your answer by $8. Probably shouldn't round until the end of the problem. I did the problem in my head, and I thought I was wrong until you showed rounding to early in the problem.

[@StephenRayWesley]

13.100

[@devonwilson5776]

Greetings. Agreed.

[@robertstuart6645]

I'm assuming the $4410 is rounded up. I computed $4402.26 using a calculator and the compound interest formula.

[@raya.pawley3563]

Thank you

[@paulbaker3527]

7000x1.05 X to the power of 10 equals $11,402.26. This sum less the $7000 is $4402.26

[@Herby-1620]

If you were a banker, your rounding might not be in line with bank policies. Banks don't round UP very much.

[@snotpu]

Here's a question: Does the bank round the result after each compounding, and if so, what would be the value of the investment after 10 years? 11402.28. I was surprised that rounding the result after each compound only affected the answer by $.02.

[@dennismayer4936]

Maybe keep on track and solve the first problem before going into solutions for "t"

[@dennismayer4936]

Kinda like giving directions to the supermarket... but , when driving home you need to go this way because there's a one way street... and the schools get out a 3 and you don't want to get stuck in that traffic.. so then I'd take a different way unless you are buying milk because the delivery guy get there late on Tuesdays so if you getting milk today before 3pm I'd probably go over here instead.

[@samjones3106]

To be more accurate - 1.05**10 = 1.629

[@russelllomando8460]

great formula. thanks.

[@danielmadden9691]

I used wrong formula, will check next time.

[@richardlong3711]

Please explain : I just worked out the above using the method of 1 year at a time adding the interest yearly. : After year 1 its 7350. After year 2 it's 7350 + 367.5 etc. After 10 years the total comes to 11,402.28. $8 short of the formulated total. On larger sums the margins will be very significant. Surely banks actually use my method over the period of any investment not the predictive formula?

[@allentiska9338]

Stop repeating! Get on with the problem!

[@dennismayer4936]

No wonder why most schools don't compete there textbooks in a year

[@aaronlichow278]

7,000×(1.05^10-1)=4,402.26

[@andrewm6424]

I saw all these people getting the answer I got and saying that you are wrong. And we are correct. You are wrong. The only way your answer is correct is if you say to round your interest rate to the nearest hundredth. PEMDAS does NOT include rounding. Without stating it in the problem, you should not have rounded until you had completed the equation fully.

[@Workingman-u7s]

A good habit to get into is to write out all the decimal points. Mr. Math Guru got lazy and fucked it up.

[@rubencastellon433]

If it is 8$ short doesn't make much difference but if it is millions ???never round up!!!

[@SorinSegal]

very nice but it could been explained and done in 3 minutes max

[@rolandogapasin812]

How much money you get per year?

[@rohiniprasad622]

Correct answer is 4402

[@danielmadden9691]

√7000= amount of money extra

[@roginutah]

Got $4,402.26

[@deograciousuwiragiye8429]

7,291.6$

[@StephenRayWesley]

13.100

[@davekearney1944]

(1.05^10 -1) × 7000 = 4402.26

[@michellestenberg6436]

I did it the oldfashioned way and got $4409. Arghhhh