# Compound Interest Calculator

parcel this Answer Link : help Paste this link in e-mail, text or social media. foremost, convert R as a percentage to r as a decimal radius = R/100 roentgen = 3.875/100 r = 0.03875 rate per year, then solve the equation for A A = P ( 1 + r/n ) nt A = 10,000.00 ( 1 + 0.03875/12 ) ( 12 ) ( 7.5 ) A = 10,000.00 ( 1 + 0.0032291666666667 ) ( 90 ) A = $13,366.37 Summary : The sum come accrued, principal plus interest, with compound interest on a principal of$ 10,000.00 at a rate of 3.875 % per year compounded 12 times per year over 7.5 years is $13,366.37 . ## Calculator Use The compound concern calculator lets you see how your money can grow using interest compound. Calculate compound interest on an investment, 401K or savings account with annual, quarterly, daily or continuous combination . We provide answers to your compound interest calculations and show you the steps to find the answer. You can besides experiment with the calculator to see how different concern rates or loanword lengths can affect how much you ‘ll pay in compound interest on a loan . Read further below for extra compound sake formula to find principal, interest rates or final investing value. We besides show you how to calculate continuous compounding with the formula A = Pe^rt . ## The Compound Interest Formula This calculator uses the compound interest formula to find principal summation sake. It uses this same recipe to solve for principal, rate or time given the other known values. You can besides use this recipe to set up a colonial pastime calculator in Excel®1 . A = P(1 + r/n)nt In the formula • A = Accrued amount (principal + interest) • P = Principal amount • r = Annual nominal interest rate as a decimal • R = Annual nominal interest rate as a percent • r = R/100 • n = number of compounding periods per unit of time • t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years. • I = Interest amount • ln = natural logarithm, used in formulas below ### Compound Interest Formulas Used in This Calculator The basic compound sake formula A = P ( 1 + r/n ) national trust can be used to find any of the other variables. The tables below show the compound interest formula rewritten therefore the obscure variable star is isolated on the left side of the equality . calculation convention Calculate accrued measure Principal + Interest A = P ( 1 + r/n ) national trust Calculate principal come Solve for P in terms of vitamin a P = A / ( 1 + r/n ) national trust Calculate principal sum Solve for P in terms of I P = I / ( ( 1 + r/n ) nt – 1 ) Calculate rate of interest As a decimal fraction r = newton ( ( A/P ) 1/nt – 1 ) Calculate rate of interest As a percentage R = roentgen * 100 Calculate time Solve for thyroxine ln is the natural logarithm triiodothyronine = ln ( A/P ) / n ( ln ( 1 + r/n ) ), then besides thyroxine = ( ln ( A ) – ln ( P ) ) / n ( ln ( 1 + r/n ) ) calculation formula Calculate accrued come Principal + Interest A = P ( 1 + radius ) deoxythymidine monophosphate Calculate principal total Solve for P in terms of a P = A / ( 1 + roentgen ) thymine Calculate principal sum Solve for P in terms of I P = I / ( ( 1 + gas constant ) t – 1 ) Calculate rate of interest As a decimal fraction radius = ( A/P ) 1/t – 1 Calculate pace of concern As a percentage R = roentgen * 100 Calculate time Solve for thyroxine ln is the natural logarithm deoxythymidine monophosphate = ln ( A/P ) / ln ( 1 + roentgen ), then besides deoxythymidine monophosphate = ( ln ( A ) – ln ( P ) ) / ln ( 1 + roentgen ) calculation formula Calculate accrued measure Principal + Interest A = Pert Calculate principal measure Solve for P in terms of a P = A / earth-received time Calculate principal total Solve for P in terms of I P = I / ( earth-received time – 1 ) Calculate rate of interest As a decimal ln is the natural logarithm roentgen = ln ( A/P ) / deoxythymidine monophosphate Calculate rate of interest As a percentage R = gas constant * 100 Calculate time Solve for metric ton ln is the natural logarithm metric ton = ln ( A/P ) / radius ### How to Use the Compound Interest Calculator: Example Say you have an investment report that increased from$ 30,000 to $33,000 over 30 months. If your local anesthetic bank offers a savings score with day by day compounding ( 365 times per year ), what annual interest rate do you need to get to match the rate of retort in your investment account ? In the calculator above blue-ribbon “ Calculate Rate ( R ) ”. The calculator will use the equations : roentgen = normality ( ( A/P ) 1/nt – 1 ) and R = r*100 . record : • Total P+I (A):$33,000
• Principal (P): $30,000 • Compound (n): Daily (365) • Time (t in years): 2.5 years (30 months equals 2.5 years) Showing the exercise with the formula radius = n ( ( A/P ) 1/nt – 1 ) : $r = 365 \left(\left(\frac{33,000}{30,000}\right)^\frac{1}{365\times 2.5} – 1 \right)$ $r = 365 (1.1^\frac{1}{912.5} – 1)$ $r = 365 (1.1^{0.00109589} – 1)$ $r = 365 (1.00010445 – 1)$ $r = 365 (0.00010445)$ $r = 0.03812605$ $R = r \times 100 = 0.03812605 \times 100 = 3.813\%$ \ [ r = 365 \left ( \left ( \frac { 33,000 } { 30,000 } \right ) ^\frac { 1 } { 365\times 2.5 } – 1 \right ) \ ] \ [ gas constant = 365 ( 1.1^\frac { 1 } { 912.5 } – 1 ) \ ] \ [ radius = 365 ( 1.1^ { 0.00109589 } – 1 ) \ ] \ [ gas constant = 365 ( 1.00010445 – 1 ) \ ] \ [ r = 365 ( 0.00010445 ) \ ] \ [ r = 0.03812605 \ ] \ [ R = r \times 100 = 0.03812605 \times 100 = 3.813\ % \ ] Your answer : R = 3.813 % per year so you ‘d need to put$ 30,000 into a savings account that pays a rate of 3.813% per year and compounds concern daily in order to get the same recurrence as the investment account .

## How to Derive A = Pert the Continuous Compound Interest Formula

A coarse definition of the changeless e is that :
$e = \lim_{m \to \infty} \left(1 + \frac{1}{m}\right)^m$
\ [ einsteinium = \lim_ { megabyte \to \infty } \left ( 1 + \frac { 1 } { molarity } \right ) ^m \ ] With continuous compound, the number of times compounding occurs per time period approaches eternity or newton → ∞. then using our original equality to solve for A as normality → ∞ we want to solve :
$A = P{(1+\frac{r}{n})}^{nt}$ $A = P \left( \lim_{n\rightarrow\infty} \left(1 + \frac{r}{n}\right)^{nt} \right)$
\ [ A = P { ( 1+\frac { gas constant } { n } ) } ^ { national trust } \ ] \ [ A = P \left ( \lim_ { n\rightarrow\infty } \left ( 1 + \frac { radius } { north } \right ) ^ { national trust } \right ) \ ] This equation looks a little like the equation for e. To make it look more similar so we can do a substitution we introduce a variable star thousand such that m = n/r then we besides have n = mister. notice that as nitrogen approaches eternity indeed does m .
Replacing nitrogen in our equation with mister and cancelling r in the numerator of r/n we get :
$A = P \left( \lim_{m\rightarrow\infty} \left(1 + \frac{1}{m}\right)^{mrt} \right)$
\ [ A = P \left ( \lim_ { m\rightarrow\infty } \left ( 1 + \frac { 1 } { thousand } \right ) ^ { mrt } \right ) \ ] Rearranging the exponents we can write :
$A = P \left( \lim_{m\rightarrow\infty} \left(1 + \frac{1}{m}\right)^{m} \right)^{rt}$
\ [ A = P \left ( \lim_ { m\rightarrow\infty } \left ( 1 + \frac { 1 } { thousand } \right ) ^ { megabyte } \right ) ^ { rt } \ ] Substituting in east from our definition above :
$A = P(e)^{rt}$
\ [ A = P ( e ) ^ { rt } \ ] And last you have your continuous compounding rule .
$A = Pe^{rt}$
\ [ A = Pe^ { rt } \ ] farther Reading
Tree of mathematics : continuous Compounding
Wikipedia : compound Interest

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