Question

Annuity A pays 1 at the beginning of each year for three years. Annuity B pays 1 at the end of each year for four years. The Macaulay duration of Annuity A at the time of purchase is 0.93. Both annuities offer the same yield rate. Calculate the Macaulay duration of Annuity B at the time of purchase.

Answer 1

Answer:

Calculate the Macaulay duration of Annuity B at the time of purchase is 1.369.

Step-by-step explanation:

First, we use 0.93 to calculate the v which equals 1/(1+i).

$\frac{0+1*v+2v^{2} }{1+v+v^{2} }$ = 0.93

After rearranging the equation, we get 1.07$v^{2}$ + 0.07v - 0.93=0

So, v=0.9

Mac D: $\frac{0+1*v+2*v^{2}+ 3*v^{2} }{1+v+v^{2}+ v^{3} }$

After substituting the value of v, we get Mac D = 1.369.