how does interest compounded daily and paid monthly work?

[jimjohn]

sorry guys this is a stupid question:

i thought if its compound interest, that means it always gets reinvested and you never get paid vs. simple interest you always get paid and nothing gets reinvested. but just wondering how this works then? it gets reinvested every day and then after the month ends, you get paid everything and then you're back to your original balance from when the month first started invested? thanks a lot!

[NetSkyBlue]

You have the first part right, your interest is reinvested and then future interest payments are calculated based on your original principal, plus all interest payments.

For example, if you invest $10,000.00 at 3% for one year, simple interest, you would have $10,300.00 at the end of the year.

If your interest is compounded monthly, then each month they add your interest payment to your principal, so the interest you earn will be just a little bit more. Your $10,000.00 after one year would now be $10,304.16.

If your interest is compounded daily, you would have 10,304.53.

To illustrate, say you invest your $10,000.00 in January. In February, they multiply the $10,000.00 by the 3% and divide by 12 (for 12 months), meaning you have earned $25. You now have $10,025.00. In March, they multiply your $10,025.00 by 3% and divide by 12, earning you $25.06 in interest (notice how you earned more interest this month, because the balance was bigger?) And it goes on and on like that. This would happen daily if your interest is compounded daily.

Basically, the more frequently the interest is compounded, the more you will earn.

So your $10,000.00 being invested at 3% for 50 years with interest compounded annually would be worth $43,839.06.
Monthly, $44,733.08
Daily, $44,814.13

[GrimJack]

A really nice 'rule of thumb' for compounding is the rule of 72; if you want to know how long it will take for your investment to double in value, divide 72 by the interest rate expressed as a %age. So if you have 10,000 invested at 3% divide 72 by 3 and it will take 24 years to get 20,000 and another 24 years to get 40,000.

Or you could ask how much interest must I get to double in 10 years - divide 72 by 10 to get 7.2, so you must invest your 10,000 at 7.2% to get 20,000 in 10 years.

The actual compounding formula is
a = p×(1 + r÷n)^n×t
p = 10000
r = .03
n = 365
t = 1
A = final amount
P = principal amount (initial investment)
r = annual nominal interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

[jimjohn]

thanks a lot guys! i now understand how daily compounding works, except i still don't understand the "paid monthly" part. how does a savings account that compounds daily but paid monthly works? from my understanding, if it compounds daily, then every day, the interest you earn is reinvested. so you never actually get paid anything back until you redeem or close the account. does this make sense guys? i just don't understand what is paid monthly? let's say i have invested 1000 dollars at 5% and it is compounded daily and paid monthly. after 1 month i will have 1004.12. so i've earned 4.12 in the first month. now am i paid this 4.12? or is this 4.12 reinvested now? thanks again guys, really appreciate the answers!

[jpg7n16]

thanks a lot guys! i now understand how daily compounding works, except i still don't understand the "paid monthly" part. how does a savings account that compounds daily but paid monthly works? from my understanding, if it compounds daily, then every day, the interest you earn is reinvested. so you never actually get paid anything back until you redeem or close the account. does this make sense guys? i just don't understand what is paid monthly? let's say i have invested 1000 dollars at 5% and it is compounded daily and paid monthly. after 1 month i will have 1004.12. so i've earned 4.12 in the first month. now am i paid this 4.12? or is this 4.12 reinvested now? thanks again guys, really appreciate the answers!

Most likely, what you are dealing with is a bank account/CD that stated say 5% APY compounded daily and paid monthly. Is that correct?

Essentially, what that means is that they calculate your interest daily, use the account balance plus accrued interest to compound, but only officially credit your account at the end of the month. And if you do that for a full year, you would have a 5% return.

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If you wanna be a math nerd like me, you can solve for the rate of interest you earn each day by saying:
1.05 = (1+x)^365 ; therefore X% = [1.05^(1/365)] - 1 = rate of interest per day.

You'd earn 0.013368% per day, which if you compound that 365 times, will get you 5% for a year.

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Here's an example with numbers for your scenario.

A 5% account that compounds daily, and pays monthly, would look like this:

Month 1 (31 days)
Day 0: Balance - $10,000; accrued interest $0
Day 1: Balance - $10,000; accrued interest $1.34
Day 2: Balance - $10,000; accrued interest $2.67
Day 3: Balance - $10,000; accrued interest $4.01
....
Day 31: Balance - $10,000; accrued interest $41.52
--pays interest of $41.52--

New Balance: $10,041.52

Month 2 (30 days)
Day 0: Balance - $10,041.52; accrued interest $0
Day 1: Balance - $10,041.52; accrued interest $1.34
Day 2: Balance - $10,041.52; accrued interest $2.68
Day 3: Balance - $10,041.52; accrued interest $4.03
....
Day 30: Balance - $10,041.52; accrued interest $40.35
--pays interest of $40.35--

New Balance: $10,081.87

[jimjohn]

thanks a lot jpg that makes sense now!