Compound Interest Formula (Example) Symbolic Formula in Excel Format Interpretation A(t) = P*(1+r/n)^(n*t) If an initial amount P grows at an annual rate r with n compoundings per year, then the value A(t) of that amount after t years is given by the right-hand side of the formula. Sample problem: An initial balance of $4,000 grows at a rate of 12.3% compounded quarterly.What is the balance after 5 years? Inputs: Formatting instructions: P = ?? r = ?? n = ?? t = ?? Dollar amounts: format as Currency with 2 decimal places $4,000.00 12.3% 4 5 Rate: format as Percentage with 1 decimal place Application of the formula to the inputs: A(t) = ?? $7,330.39 Periods/Years: format at Number with 0 decimal places Future Value of Periodic Payments Symbolic Formula in Excel Format Interpretation A(t) = P*((1+r/n)^(n*t)-1)/(r/n) If an amount P is contributed at the end of each of n periods per year and the balance earns interest at an annual percentage rate of r, the total amount A accrued after t years is given by the right-hand side of the formula. Sample problem: An amount of $250 is contributed at the end of each month, and the balance earns interest at an APR of 6.2%.What is the total amount accrued after 7 years? Inputs: Formatting instructions: Dollar amounts: format as Currency with 2 decimal places Rate: format as Percentage with 1 decimal place Application of the formula to the inputs: Periods/Years: format at Number with 0 decimal places Loan Payment Formula Symbolic Formula in Excel Format Interpretation PMT = P*(r/n)/(1 - (1 + r/n)^(-n*t)) The amount PMT that must be paid n times per year for t years to pay off a loan principal amount of P at an APR of r is given by the right-hand side of the formula. Sample problem:What is the monthly payment amount needed to pay off a loan principal amount of $10,000 over 4 years, given an interest rate of 7.3%? Inputs: Formatting instructions: Dollar amounts: format as Currency with 2 decimal places Rate: format as Percentage with 1 decimal place Application of the formula to the inputs: Periods/Years: format at Number with 0 decimal places Inflation Rate Formula Symbolic Formula in Excel Format Interpretation IR = (new CPI - old CPI)/(old CPI) Given an old CPI value at one point and a new CPI value n years later, the n-year inflation rate IR is given by the right-hand side of the formula. Sample problem: The CPI value in January 2009 was 211.143; the CPI value in January 2014 was 233.916.What was the 5-year inflation rate between January 2009 and January 2014? Inputs: Formatting instructions: CPI values: format as Number with 3 decimal places Inflation rate: format as Percentage with 3 decimal places Application of the formula to the inputs: