Future & Present Value of an Annuity UNIT 6 FINANCE

Regular Annuity  When the payments are due at the end of the period:  FV = future value  Pmt = fixed payment or deposit  i = annual interest rate  n= number of compounded periods per year  T = number of years

 What amount will accumulate if we deposit $5,000 at the end of each year for the next 5 years? Assume an annual interest rate of 6% compounded annually.  FV=  Pmt =  t=  i =  n =

Annuity due  When the payments are due at the beginning of the period:  FV = future value  Pmt = fixed payment or deposit  i = annual interest rate  n= number of compounded periods per year  T = number of years

 What amount will accumulate if we deposit $5,000 at the beginning of each year for the next 5 years? Assume an annual interest rate of 6% compounded annually.  FV=  Pmt =  t∙n=  i =

Present Value of a Regular Annuity  When the payments are due at the end of the period:  PV = present value  Pmt = fixed payment or deposit  i = annual interest rate  n = number of compounded periods per year  t = number of years

 Calculate the present value of an annuity of $500 paid at the end of each month. The annual interest rate is 12% compounded monthly for two years.  PV=  Pmt =  t∙n(N)=  i =

Present Value of Annuity due  When the payments are due at the beginning of the period:  PV = present value  Pmt = fixed payment or deposit  i = annual interest rate  n = number of compounded periods per year  t = number of years

 Calculate the present value of an annuity of $500 paid at the beginning of each month. The annual interest rate is 12% compounded monthly for two years.  PV=  Pmt =  t∙n (N)=  i =

TVM Solver  Press Apps to access the Finance tool and press enter

TVM Solver  Next press enter on the TVM Solver

TVM Solver  N = n ∙ t  I% = is the interest rate or APR in percent not decimal  PV is the present value  PMT is the payment  FV is the future value  P/Y & C/Y is the compounding periods per year which is n  Note the PMT: End Begin is used especially with annuities.

TVM Solver Example  This is a $250 investment with a 5 percent interest rate and is compounded monthly. This investment is for 3 years.  N is n ∙ t  Payment is 0 because there is no monthly payment there is no monthly payment  We will solve for FV using TVM solver TVM solver

TVM Solver  While the cursor is on Line FV Press Alpha then Enter

TVM Solver  The Future value of this investment is $290.37