If I was given an amount of money for 1 month, and I wanted to compound its interest monthly, which formula would I need to use?
My interest rate is 2.5%. I want to compound monthly (so n=12). But I want to find the amount after compounding interest monthly FOR THAT single month. The amount I'm give (which I think would be P) is 18.60, and is specifically for the month of January.
If I'm using the A=P(1+(r/n))^nt how would I plug my information in?
Like this: A=18.6(1+(.025/12))^(12)(1/12)
Or
Like this: A=18.6(1+(.025/12))^(12)(1)
don't make it look so complicated
i = .025/12 = .00208333.. (I use my calculator's memory to store such numbers, don't round them off yet)
amount = 18.6(1.00208333...)^1 , for 1 month
= 18.6(1.00208333..
= $ 18.64
Wow, we gained 4 cents interest !
THANK YOU SO MUCH! :)
Actually, one more quick question. Then if I were going to compound the interest continuously, would it be
A=18.6e^(.025)(1/12)
yes, it would be 18.6387
since the time is so short, it is no surprise that the two answers are the same
To calculate the amount you will have after compounding the interest monthly for a single month, you can use the formula A = P(1 + r/n)^(nt), where:
A represents the final amount you will have.
P represents the initial amount you were given, which is $18.60 in this case.
r represents the interest rate in decimal form, which is 2.5% or 0.025.
n represents the number of times the interest is compounded per year, which is 12 since you want to compound monthly.
t represents the time in years, but since you want to calculate for a single month, t will be 1/12.
Therefore, plugging in your values into the formula, it would be written as:
A = 18.6(1 + (0.025/12))^((12)(1/12))
Simplifying this expression:
A = 18.6(1 + (0.0020833333333333))^1
Which further simplifies to:
A = 18.6(1.0020833333333333)
A ≈ 18.624688
So, the amount you will have after compounding the interest monthly for a single month would be approximately $18.62.