How do calculate the compound interest formulae
Answers
A = P(1 + r/n)nt
Where:
A = Accrued Amount (principal + interest)P = Principal AmountI = Interest AmountR = Annual Nominal Interest Rate in percentr = Annual Nominal Interest Rate as a decimalr = R/100t = 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 periodCompound Interest Formulas and Calculations:Calculate Accrued Amount (Principal + Interest)A = P(1 + r/n)ntCalculate Principal Amount, solve for PP = A / (1 + r/n)ntCalculate rate of interest in decimal, solve for rr = n[(A/P)1/nt - 1]Calculate rate of interest in percentR = r * 100Calculate time, solve for tt = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]
A = Pe^rt.
Compound Interest EquationA = P(1 + r/n)nt
Where:
A = Accrued Amount (principal + interest)P = Principal AmountI = Interest AmountR = Annual Nominal Interest Rate in percentr = Annual Nominal Interest Rate as a decimalr = R/100t = 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 periodCompound Interest Formulas and Calculations:Calculate Accrued Amount (Principal + Interest)A = P(1 + r/n)ntCalculate Principal Amount, solve for PP = A / (1 + r/n)ntCalculate rate of interest in decimal, solve for rr = n[(A/P)1/nt - 1]Calculate rate of interest in percentR = r * 100Calculate time, solve for tt = 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)tCalculate Principal Amount, solve for PP = A / (1 + r)tCalculate rate of interest in decimal, solve for rr = (A/P)1/t - 1Calculate rate of interest in percentR = r * 100Calculate time, solve for tt = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)Continuous Compounding Formulas (n → ∞)Calculate Accrued Amount (Principal + Interest)A = PertCalculate Principal Amount, solve for PP = A / ertCalculate rate of interest in decimal, solve for rr = ln(A/P) / tCalculate rate of interest in percentR = r * 100Calculate time, solve for tt = 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 in years): 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.
