Compound Interest Calculator

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Compound Interest Calculator
Calculate:
Where: A = P(1 + r/n)nt

Principal (P): $
Rate (R):   %
Compound (n):  
Time (t):   years

Answer:

A = $ 13,366.37

Compound Interest Equation

Current Calculation:
A = P(1 + r/n)nt

Where:

  • A = Accrued Amount (principal + interest)
  • P = Principal Amount
  • I = Interest Amount
  • R = Annual Nominal Interest Rate in percent
  • r = Annual Nominal Interest Rate as a decimal
  • r = R/100
  • t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
  • n = number of compounding periods per unit t; at the END of each period

Compound Interest Formulas and Calculations:

  • Calculate Accrued Amount (Principal + Interest)
    • A = P(1 + r/n)nt
  • Calculate Principal Amount, solve for P
    • P = A / (1 + r/n)nt
  • Calculate rate of interest in decimal, solve for r
    • r = n[(A/P)1/nt - 1]
  • Calculate rate of interest in percent
    • R = r * 100
  • Calculate time, solve for t
    • t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]

Formulas where n = 1 (compounded once per period or unit t)

  • Calculate Accrued Amount (Principal + Interest)
    • A = P(1 + r)t
  • Calculate Principal Amount, solve for P
    • P = A / (1 + r)t
  • Calculate rate of interest in decimal, solve for r
    • r = (A/P)1/t - 1
  • Calculate rate of interest in percent
    • R = r * 100
  • Calculate time, solve for t
    • t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)

Continuous Compounding Formulas (n → ∞)

  • Calculate Accrued Amount (Principal + Interest)
    • A = Pert
  • Calculate Principal Amount, solve for P
    • P = A / ert
  • Calculate rate of interest in decimal, solve for r
    • r = ln(A/P) / t
  • Calculate rate of interest in percent
    • R = r * 100
  • Calculate time, solve for t
    • t = ln(A/P) / r

Example Calculation

I have an investment account that increased from $30,000 to $33,000 over 30 months.  If my local bank offers savings account with daily compounding (365), what annual interest rate do I need to get from them to match the return I got from my investment account?

In the calculator select "Calculate Rate (R)". The equation the calculator will use is: r = n[(A/P)1/nt - 1] and R = r*100.

Enter:
Total P+I (A): $33,000
Principal (P): $30,000
Compound (n): Daily (365)
Time (t): 2.5 years (2.5 years is 30 months)
Your Answer: R = 3.8126% per year

Interpretation: You will need to put $30,000 into a savings account that pays a rate of 3.8126% per year and compounds interest daily in order to get the same return as your investment account.

 

Cite this content, page or calculator as:

Furey, Edward "Compound Interest Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.