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).
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...
Homework Statement
Amy deposited $1000 into an account that earns 8% annual interest compounded every 6 months. Bod deposited $1000 into an account that earns 8% annual interest compounded quarterly. If neither Amy nor Bob makes any additional deposits or withdrawals in 6 months, how much more...
Homework Statement
The constant ##e## can be defined in many ways. My first exposure to this number involved compound interests. Specifically, if you decide to continuously compound 1$ at a 100% interest rate for a certain period of time(year, month, etc), you'll end up with ##e##$ where it is...
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 = ...
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...
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...
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%?
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]
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!
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...
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 =...
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)...
- 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...
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...
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...
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...
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...
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...
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 +...
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...
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...
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...
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...
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 *...
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...
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...
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...
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...
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
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...
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...
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 $60,000 increasing by 3% inflation each year (so the...
Is there any equation/formula for continuous compound interest to which money is added (or substracted from) periodically? Or can one be derived?
Thanks
i.e. monthly interest rate is 50% and we add 1$ every month (:bugeye:)
Initially: 1$
1st Month: 1.6 + 1 = 2.6$
2nd month: 4.3 + 1...
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...
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.
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...
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...