Question

The future value of an ordinary annuity stream of $185 periodic payment per year is $982.19 when valued at a 3% rate. By approximately how much would the future value change if this is annuity due and interest rate remains at 3%?

Answer 1

Annuity is a series of payments made or received over a period of time This can be divided into two parts, 1) Ordinary Annuity : In an ordinary annuity payments are made at the end of the period. 2) Annuity Due: In annuity Due Annuity payments are at the Beginning. i.e as soon as the annuity begins. Explanation: When we receive a Dollar today value of the same increases at the end of the end of the period. Hence dollar Received at the beginning of the year should be brought to the Future Value at the end of the period. Future Value as per Annuity Stream i.e Ordinary Annuity. Year FV Factor 1 Annual Payment $185 $185 $185 2 3 1.000 1.030 1.061 1.093 1.126 Total Future Value $185.000 $190.550 $196.267 $202.154 $208.219 $982.190 4 $185 5 $185 Here Stream of cashflows begins at the end of the period Future Value as per Annuity Due. Year Annual Payment 1 $185 2 $185 3 $185 4 $185 5 $185 FV Factor 1.030 1.061 1.093 1.126 1.159 Total Future Value $190.550 $196.267 $202.154 $208.219 $214.466 $1,011.656 Here Stream of cashflows begins at the Beginning of the period Difference Between these two ($ 1011.656-$ 982.190 ) is $29.466. Value changes by $29.466