I’m currently watching the percent-ratio video on week 1 day 2 (part 2). In this video (@47:12), you are doing and explaining a problem on compound interest, which is the following:

“if an initial amount of $1000 has an annual interest rate of 12% and compounded every 3 months, what will be the result after a year ?”

when solving, you had 1000(1.04)^4. you explained that the principal is compounded every 3 months thus the result 1.04, which I understand comes from (1+(0.12)/3). However, I think there’s a mistake there about the number of times the interest is compounded.

This is my reasoning:

every 3 months = quarterly -> interest is compounded 4 times in a year thus, the new interest becomes r’= 0.12/4=0.03 thus 1+0.3

therefore the final amount will be A=1000(1.03)^(4*1). with 1 in this case representing the number of years.

Hey @jai Jai ! you’re actually confirming my reasoning. I was pointing out to Greg and those who are watching the Fraction, percent video (part2) in the quant concept series that he might have made a mistake when solving this problem during the video.

@jai if that’s the case then I still do think it doesn’t make sense.
let’s try with the actual formula A= P(1+r/m)^(mt), where :
A is the future value
P: the principal
m: the number of times the interest is compounded in a year
r: the annual interest rate
t: the number of years

the interest rate is compounded 4 times in a year meaning that m=4 .
if the interest is compounded every 3months then within a year of 12 months it is compounded exactly 4times (3months +3months +3months +3months ).
the annual interest rate r=0.12 . the time t=1year the principal P=$1000

thus the future value = $1000(1+0.12/4)^(4*1)

@sisi compounded every 6months means it is compounded twice “(6+6)” in a year

also Jai, I’m noticing that we do have the same formula and use also come up with 4 times in a year.
what I’m not getting is that you come up with n=4 , you have the formula where you can plug the number n=4 but instead you use n=3 when it comes to r/n but then use n=4 when it comes to nt ?..

@sisi so that you don’t make this mistake on this kind of problem in the future but think of compound interest like a membership to a program you signed up for in a year but without all the fees (interest ).
For example, you have a swimming membership plan that you signed up for. the subscription rate is that they charge you $X every 6 months. in other words at the end of a year (a year =12 months ), you’ll be charged two times for that swimming membership.
that is, the first six months you pay $X, the second 6months you pay another $X.

compound interest is almost the same just that you might have interest fees on top of that second subscription charge.

also, the issue I was having with Jai, or this problem in general, was not the number of times the interest was compounded but the fact that we all agreed that the compounded times was 4 and that a mistake was made when plugging in that number in the future value formula A= P(1+r/m)^(m*t)