The formula for the present value of an annuity due is
A) $C \times \left[ \left( p _ { 0 _ { r _ { 1 } } } \right) \left( p _ { k , t } \right) \right]$

B) $C \times \left[ \frac { 1 - \frac { 1 } { ( 1 + i ) ^ { n } } } { i } \right]$

C) $C \times \left[ \frac { 1 - \frac { 1 } { ( 1 + i ) ^ { n - 1 } } } { i } + 1 \right]$

D) $C \times \left[ \frac { ( 1 + i ) ^ { n } - 1 } { i } \right]$

Question

The formula for the present value of an annuity due is
A) $C \times \left[ \left( p _ { 0 _ { r _ { 1 } } } \right) \left( p _ { k , t } \right) \right]$

B) $C \times \left[ \frac { 1 - \frac { 1 } { ( 1 + i ) ^ { n } } } { i } \right]$

C) $C \times \left[ \frac { 1 - \frac { 1 } { ( 1 + i ) ^ { n - 1 } } } { i } + 1 \right]$

D) $C \times \left[ \frac { ( 1 + i ) ^ { n } - 1 } { i } \right]$

Quizplus · Accepted Answer

The present value of an annuity due is calculated by adjusting the present value of an ordinary annuity formula to account for the fact that payments are made at the beginning of each period. This is done by multiplying the ordinary annuity formula by (1 + i), which is reflected in choice C.

The Formula for the Present Value of an Annuity Due C×[(p0r1)(pk,t)]C \times \left[ \left( p _ { 0 _ { r _ { 1 } } } \right) \left( p _ { k , t } \right) \right]C×[(p0r1​​​)(pk,t​)]

The Formula for the Present Value of an Annuity Due $C \times \left[ \left( p _ { 0 _ { r _ { 1 } } } \right) \left( p _ { k , t } \right) \right]$