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. B

    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. opus

    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. Z

    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. M

    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. Schaus

    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. L

    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. J

    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. P

    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. alexandria

    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. alexandria

    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. W

    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. C

    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?
  14. T

    [Compound Interest] Layman way vs. Derivative way

    My https://www.amazon.com/dp/0073532320/?tag=pfamazon01-20 (p. 176 Example 7.1) pointed out that an investment ##p(t) = 100\,2^t## (##t## in year) that doubles the capital every year starting with an initial capital of $100, has an (instantaneous) rate-of-change ##\frac{\text{d}}{\text{d}t} p(t)...
  15. S

    Compound Interest Paid in 3.5 Years: Regional Laws & Concepts

    - This may be a stupid question as I am totally new to the concept of interest. I don't even know if my question is valid. - Figure is given below for referenceSuppose I deposit some money in a bank that pays compound interest on yearly basis. If I decide to withdraw my amount at the end of 3.5...
  16. C

    Differential Equations : Compound Interest

    Homework Statement A college student wants to start a new savings account with an initial balance of $0. He plans to save money at a continuous rate of $700 per month. Additionally, every month he plans to increase this rate by $7. (Such that for example in month 3 he is saving at rate $721...
  17. gfd43tg

    Compound interest loops problem (matlab)

    Homework Statement (a) Suppose you decide to invest money in a Certificate of Deposit (CD). Write code that assigns to the variable FinalValue the final value of the CD based on the following variables: Investment: the initial amount of money invested in the CD, Rate: the annual...
  18. A

    Is there any way to derive an equation for compound interest based

    Is there any way to derive an equation for compound interest based on effective interest rate instead of the nominal interest rate?
  19. A

    What is the effective interest rate per period for compounding semiannually?

    Homework Statement I have borrowed $100. The interest rate is 5% per year compounded semiannually. How much will I have to pay the bank after 1 year? Homework Equations ##F=P(1+i)^{ n }##, where i is the effective interest rate per period and n represents the number of periods The Attempt...
  20. H

    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. H

    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. H

    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 +...
  23. ShawnD

    Derivative of the compound interest equation

    I'm trying to prove a point to someone about compounding periods and mortgage payments. Interest is calculated as $ = P(1 + I/x)^x where P is how much you borrowed, I is "annualized" interest rate and x is how many compound periods are in a year. For example, a credit card at 20% compounded...
  24. G

    Compound Interest Formula and Natural Logarithms

    Homework Statement Solve the compound interest formula for r by using natural logarithms. Homework Equations A=P(1+r/n)nt The Attempt at a Solution 1400 = 1000(1+r/360)(360*2) 1.4 = (1+r/360)720 ln(1.4) = 720ln((360+r)/360) I'm not sure where to go after this. Did I...
  25. nomadreid

    Radioactive decay versus compound interest

    The fact that radioactive decay and continuous compound interest end up with the same formula (with the "rate" being negative in the former and positive in the latter) seems to me to be more a result of the ubiquity of the exponential function in solving differential equations than any common...
  26. T

    Compound Interest With Repayments problem

    1. A 30 year old employee on a starting salary of $20 000 per year pays 5% of this into a superannuation scheme to which the employer also contributes 5% of the employee’s salary. If the fund is compounding at 5% p.a., find the lump sum payout when the employee retires at 60. Note: This...
  27. A

    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 *...
  28. L

    Continuous compound interest with additional transactions

    1. The accountants at HR office of the Sirius Cybernetics Corporation have determined that the company would need additional $10 billion in its pension fund account over and above the current projected amount at the end of year 2030. (a) Assuming the fund's balance will be growing, compounds...
  29. A

    Calculating Compound Interest: January 2010 Cash Balance Analysis

    Homework Statement January 1, 2010, opening cash balance is $20590.17. January 31, 2010, closing cash balance is $20626.89. Interest rate is 2.1%. Interest paid is $36.72. (There are 31 days in January 2010). I=interest A=amount (ie. P+I) P=principal i=interest rate per...
  30. M

    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. L

    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. F

    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
  33. I

    Compound Interest / Annuities problem

    Suppose that you are negotiating your bonus with your boss. She offers you three options for your bonus: Option A: You get $5000 right now Option B: You get 8 monthly payments of $650 starting 1 month from now Option C: You get $5300, but you have to wait 8 months before you get it Using an...
  34. D

    Financial, Multiple Compound Interest Problem

    I am currently attempting to solve the following problem for a calculator I am constructing in Java. Company 1 pays A% Interest every T days Company 2 pays B% Interest (>A%) every T days Company 1 has an initial investment of $X dollars Company 2 requires an inital fee of $Y dollars to...
  35. N

    Inflation-complicated compound interest

    Hi gang, I need help with a formula if somebody with an enormous brain and generous heart has some spare time. I need to work out what 9% of $60,000 ($5400) invested annual at 7% (net of fees and taxes) would grow to in 30 years, with the $60,000 increasing by 3% inflation each year (so the...
  36. C

    Continuous Compound Interest with changing capital

    Is there any equation/formula for continuous compound interest to which money is added (or substracted from) periodically? Or can one be derived? Thanks i.e. monthly interest rate is 50% and we add 1$ every month (:bugeye:) Initially: 1$ 1st Month: 1.6 + 1 = 2.6$ 2nd month: 4.3 + 1...
  37. O

    Help with Compound Interest Homework Problem

    i have five problems on this on my econ test tomorrow. PLEASE HELP! I've looked in my book and can't find anything! thank you :) Homework Statement Calculate compound interest: principal: 65,000 rate: 5.25% time: 1.5 years it doesn't say how long it's going to be compounded...
  38. K

    Compound Interest: Grow $1000 to $1500 in 5 Years?

    At what rate of interest compounded quarterly, to the nearest tenth of a percent, will an investment of $1000 grow to $1500 in 5 years? I set the problem up 1500=1000(1+x/4)^(4*5) I then divided by 1000 1.5 = (1+x/4)^20 But this is where I'm stuck.
  39. P

    Formula for Compound Interest

    Hello, I wanted to know is there a formula for compound interest when making additional payments. i.e. I make payments of $500 ever year for 5 years and NOT just $2500 once for the 5 year term. The current way I am calculating the result is using Compound Interest of initial payment for one...
  40. S

    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...