# What is Compound interest: Definition and 40 Discussions

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).

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1. ### Compound Interest: 3.11% Annually, 3x/Year

1. 350*(1+(0.0311)/3)*ln(1+(0.0311)/3) 2 and 3. Not sure how to answer these questions.
2. ### B Question about Compound Interest Formula

If I have an investment, that is compounded at some rate ##r##, ##n## times per year, it can be written as a function as such: $$A(t)=P\left(1+\frac{r}{n}\right)^{nt}$$ My question is in regards to the 1 here. I think I have a general idea of what it's for, but I can't really put it into...
3. ### Compound Interest Homework: Amy vs Bob

Homework Statement Amy deposited $1000 into an account that earns 8% annual interest compounded every 6 months. Bod deposited$1000 into an account that earns 8% annual interest compounded quarterly. If neither Amy nor Bob makes any additional deposits or withdrawals in 6 months, how much more...
4. ### Show that ##\lim_{n\to\infty}(1+\frac{r}{n})^n=e^r##

Homework Statement The constant ##e## can be defined in many ways. My first exposure to this number involved compound interests. Specifically, if you decide to continuously compound 1$at a 100% interest rate for a certain period of time(year, month, etc), you'll end up with ##e##$ where it is...
5. ### Logarithm question using compound interest formula

Homework Statement A colony of ants will grow by 12% per month. If the colony originally contains 2000 ants how long will it take for the colony to double in size? Answer - 6.12 months Homework Equations A = P(1+r/n)nt The Attempt at a Solution r = 12% = 0.12 n = 12 P = 2000 A = 4000 t = ...
6. ### MHB Calculate Compound Interest: Easy Step-by-Step Guide | Calculator Tips

Hi new to the forum and would like to improve my level of maths. I am working through a text but need some help with a compound interest question. the formula to find compound interest is I = P (1 + R)n–1. P= principal sum R= interest rate n= number of periods for which interest is calculated...
7. ### MHB Compound Interest C programming problem

Hello everyone, i hate that i can't figure this out and I'm just looking for good direction on how to figure out the last bit of my code. I'm first time user of C programming and haven't fully grasp the concepts and tools available to me so be patient if you offer any help. My task is to write a...
8. ### MHB Compound Interest Problem: When Will Mr. Weasley's Liabilities Be Cancelled?

Can anyone help me with this problem? I'm stuck When will a payment of 300,000 galleons cancel Mr. Weasley’s liabilities to Gringott’s Bank of 100,000 galleons due after 2 years and 150,000 galleons due after 5 years if money is worth at an effective rate of 12%?
9. ### Exponential growth and compound interest

Homework Statement Homework Equations A = P(1+i)^n The Attempt at a Solution Here is my attempted solution, can someone please verify if my method is correct! Thanks in advance![/B]
10. ### Exponential growth and compound interest

Homework Statement Homework Equations The Attempt at a Solution here is my attempted answer, can someone please verify if my method is accurate and if my solution is correct? thanks for the help!
11. ### Compound Interest & Number e Connection

Originally (as far as I know) the number e (ie. 2.71828...) came up in compound interest calculations. For example, if you have 1 dollar, and a compound interest of 100% per year, and the interest is continuously calculated, after one year you'll have exactly e dollars. The generic formula...
12. ### Compound Interest Systems of Equations Problem

Homework Statement Romeo was given a gift of $10,000 when he turned 16. He invested it at 3% per annum. Three years later, Juliet was given$10,000, which she invested at 5% per annum. When will the two amounts be equal in value? Homework Equations Compound Interest Formula Total =...
13. M

### Interest Formula for Varying Time Units and Compoundings?

For the formula A=A0(1+r/k)^(kt) does it only work if t is in years and k is how many times per year it is compounded?

20. ### Logarithm: Compound interest problem

Homework Statement How long does it take for a sum of money to double if it is invested at 8% compounded semi-annually? Homework Equations A = P(1+i)n A: Compounded amount P: Initial amount i: Interest rate n: Period The Attempt at a Solution A = P(1+i)n (2x) = (x)[1+(0.08)]2n (2n because...
21. ### Compound interest using DE

Homework Statement Assume that Po dollars is deposited into an account paying r percent compounded continuously. If withdrawals are at an annual rate of 200t dollars (assume these are continuous) find the amount in the account after T years. The Attempt at a Solution I have two differential...
22. ### MHB Balance After 5 Years of Compound Interest on Monthly Deposits

So I'm trying to find out the formula by writing out the expanded version first and simplifying it, but I'm not sure how to write this in terms of exponents. Month 1: 25 + 25(.05) Let x = 25 + 25(.05) Month 2: (x + 50)(.05) + (x + 50) Month 3: ((x + 50)(.05) + (x + 50) + 75)(.05) + ((x +...

27. ### Compound Interest Formula and Natural Logarithms

Homework Statement Solve the compound interest formula for t by using natural logarithms. Homework Equations A=P(1+\frac{r}{n})^{nt} The Attempt at a Solution I start by dividing both sides by P. I then take the natural log of both sides and end up with ln(\frac{A}{P})=nt *...

30. ### Solve the Science Club Fundraiser Puzzle - Compound Interest

At a school fundraiser, the science club made 58% of their money selling juice, 27% selling cookies,and 15% selling appels . The club made 87% selling juice .How much did the club make selling cookies? How much did they make selling appels? Please help me figure this out i am completely lost...
31. ### Derivative of compound interest

Homework Statement f(x) = (1/x+1)^x, find f'(x) Homework Equations derivative of a^x = ln(a) a^x The Attempt at a Solution When I differentiate i get ln((1+x)/x)*((1+x)/x)^x... However, this solution does not match what I should be getting. Am i differentiating wrong at some point...
32. ### Compound interest, what is it ?

I know interest is compute by formula interest=(All money person get) - expense but I hear there say compound interest, what is it ? after all how many interest is there ? Thank you

40. ### Understanding Compound Interest: Solving Problems and Maximizing Profits

I'm having some trouble with this problem what i did was (15500 + 1000t)*e^0.05t > 1000 so basically, when the money you are making is greater than how much you would make by keeping the cards i know the first t = when you sell it, but what is the second t? that should be the amount of time...