Interest and Equivalence Chapter 3: Newnan, Eschenbach, and Lavelle Dr. Hurley’s AGB 555 Course

Time Value of Money and Interest Interest is a way of valuing money across different time periods. Simple Interest Interest that is computed on the original sum only Total interest earned after n years is P*i*n where P represents the principal, i represents interest, and n represent the number of years interest is charged

Compound Interest This is where interest is charged on interest Total interest earned after n years is P*(1+i) n – P, where P represents the principal, i represents interest, and n represent the number of years interest is charged

Equivalence Equivalence is based on the idea that you are indifferent between two different sums of money over some reference time frame So $10,000 now is said to be equivalent to $11,000 one year in the future when the expected interest rate is 10%

Single Payment Compound Amount Formula F = P(1+i) n F is the future value of a current value at the end of n periods P is the current value of money i is the interest rate per interest period n is the number of periods the interest is compounded

Single Payment Compound Amount Formula in Excel =-FV(Rate,Nper,Pmt,[Pv],[Type]) Rate is equal to the periodic interest rate (i) Nper is the number of periods (n) Pmt represents periodic payments made over time Note this should be zero for the current formula [ ] represents an optional component in the formula Pv is the current/ present value of the money (P) This is needed for the current formula Type: 0 or blank implies payment at the end of the period, 1 indicates payment at the beginning of the period

Single Payment Present Worth Formula P = F(1+i) -n P is the current value of money F is the future value of a current value at the end of n periods i is the interest rate per interest period n is the number of periods the interest is compounded

Single Payment Present Worth Formula in Excel =-PV(Rate,Nper,Pmt,[Fv],[Type]) Rate is equal to the periodic interest rate (i) Nper is the number of periods (n) Pmt represents periodic payments made over time Note this should be zero for the current formula [ ] represents an optional component in the formula Fv is the future value of the money (P) This is needed for the current formula Type: 0 or blank implies payment at the end of the period, 1 indicates payment at the beginning of the period

Nominal Interest Rate It is the annual interest rate without considering any compounding E.g., 2.5% quarterly interest rate is equivalent to a 10% annual interest rate Also known as the Annual Percentage Rate

Effective Annual Interest Rate This interest rate takes into account compounding i a = effective annual interest rate r = nominal interest rate per year m = number of compounding periods during the year Effective annual interest rate compounded continuously i a = e r - 1