2.4 Series of Investments, Annuity Due
An annuity due is when the first instalment is deposited at the beginning of the period. The formula used is: FVA = PMT x (FVIFAn;r – 1) or
FVA = PMT [(1+rn+1-1r)-1]
An investor pays equal instalments of R100 at the beginning of each year into a savings account yielding an interest rate of 12% per year, compounded annually. What is the future value of the investment at the end of three years?
In this case all three instalments earn interest. We could undertake three separate calculations and sum the results or we could adjust the Table B reading, meaning the periods would be 3 + 1, but without the first instalment i.e. we use the reading for 4 periods deducting 1 from the factor.
FVA = PMT x (FVIFA4;0.12 – 1) = R100 x (4.7793 – 1) = R377.93
Or FVA = PMT [(1+rn+1-1r)-1] = R100 [(1+ 0.124-10.12)-1] = R377.93