Using compound interest formula to making a smarter investment decision, precalculus tutorial

[@epsi]

Flipping the idea so that the money is a loan to be repaid, you'd still want $3000 @ 4% APR if you don't need that other $1000 because, practically speaking, you will be repaying such "low" amounts in 10 years or less rather than 30-ish years, which means you'll pay less overall in 10 years compared to the amount you'd pay if you chose the $4000 @ 3% APR.

[@rickguerrero2282]

A really nice problem to explore the compound interest formula!

[@philstubblefield]

Unless I'm missing something, you'll have to wait just under 30 _months_, not _years_, because the compounding period is one month. Try it in a spreadsheet or write a quick program...

[@xXJ4FARGAMERXx]

He said t is measured in years at the beginning of the video

[@omargoodman2999]

t is years, *n* is how many compounding intervals *per year;* in this case, 12 because it's monthly. So months has already been accounted for. 29.95 *years* means 29.95 * 12 compounding *intervals,* in other words 359.4 months. 359 or fewer, higher principal gives more; 360 or more, higher rate gives more.

[@PavelBukarev]

Question. Why did you divide by 12 first? You could wait and 12 on the right and 12 on the left would cancel each other. It doesn't make a significant difference in this example, but in general it's a good practice that makes calculations easier and more precise.

[@zanti4132]

For a similar math problem with some practical value, consider the question of when to start taking social security. (OK, most of you are probably many years from having to make that decision for yourselves, but maybe your parents will need to make that decision soon.) You can start taking social security at age 62, at which point you will receive P dollars each month from the government. However, you can defer receiving any money for up to 8 years, i.e. until age 70, and for each year you wait the amount you receive each month will increase by 8%. The payments to you will continue until you die. The questions are: (a) You should start social security at age 62 if you expect to die by what age? (b) If you wait until age 70, you have to live to what age to get the maximum return?

[@brouquier7172]

If you're 25 years old and you're saving for your retirement in 40 years' time, then the first option is better even if you have to wait 30 years for it to catch up with the second option 😉

[@chocolateangel8743]

People aren't trying to wait 40 until retirement, anymore. Younger people, especially, are all about the F.I.R.E. Movement (Financial Independence, Retire Early). They don't want to wait until they are old before they can start enjoying life.

[@Sg190th]

Always hated interest. Even math proves it.

[@omargoodman2999]

So you'd say you weren't... _interested?_ [Rimshot]

[@99estoc99]

Considering current instability in all matters, maybe 6 months is long indeed.

[@sanjaybhowmick4905]

Awesome lecture..and also first comment..love from india

[@fantiscious]

It would be interesting to know how many years it would to before the first option is $10,000 ahead of the second one. Sadly a closed-form of the inverse of the difference of two exponential functions doesn't exist, so no equation can be made that is solvable.

[@drpop932]

Wow 🔥👏👏👏

[@prant55]

lol

[@bertrandvandeportaele3811]

Hi! You make really nice videos! Thank you. I've done the test a=p*(1+r/n)**(n*t) to check if the two deals equate at 29.95 years and they don't. So I've investigated a bit in python and found that the roundings that you made have a not so negligible impact. Keeping the intermediate terms formula in python, I obtain: t=math.log(0.75)/(12*math.log( (1+0.03/12)/ (1+0.04/12) )) # =28.85211285631959 wich is more than a year off from yours. May be an idea for a new video about round off impact analysis ie, t=math.log(0.75)/(12*math.log( a/ b )), study dt/da and dt/db for instance. Thanks again!