Working out one of the problems in the Actex FM manual, I found myself having to solve the annuity immediate equation
500 :s_angle(5) = 100 :s_angle(10).
There is a simple way to solve this which is different from the solution that the text gives. Start with the identity a_angle(n+k) = a_angle(n) + v^k*a_angle(k) and note that if you multiply both sides by v^-1 you get the same identity for the annuity due.
Next, take that equation and multiply both sides by v^(-n-k) and you get another identity relating future values for an annuity due, which is the same identity for an annuity immediate.
In this particular problem, the identity causes the future value terms to drop out. A fairly simple equation in v results, allowing you to solve for the interest rate quickly. In case you are interested, this is sample exam problem #1 in M2.
500 :s_angle(5) = 100 :s_angle(10).
There is a simple way to solve this which is different from the solution that the text gives. Start with the identity a_angle(n+k) = a_angle(n) + v^k*a_angle(k) and note that if you multiply both sides by v^-1 you get the same identity for the annuity due.
Next, take that equation and multiply both sides by v^(-n-k) and you get another identity relating future values for an annuity due, which is the same identity for an annuity immediate.
In this particular problem, the identity causes the future value terms to drop out. A fairly simple equation in v results, allowing you to solve for the interest rate quickly. In case you are interested, this is sample exam problem #1 in M2.
Useful annuity future value formula
0 commentaires:
Enregistrer un commentaire