An insurance agent is trying to sell you an annuity, that will provide you with 10,600 at the end of each year for the next 30 years. If you don't purchase this annuity, you can invest your money and earn a return of 5%. What is the present value of the annuity?

Solution

implicit derivative

in s u r an ce a g e n t i s t ry in g t o se ll yo u an ​ ann u i t y, t ha t w i ll p ro v i d e yo u w i t h ​10, 600 a t t h e e n d o f e a c h ye a r f or t h e n e x t 30 ye a rs . I f yo u ​ d o n^{'} t p u rc ha se t hi s ​ ann u i t y, yo u c an in v es t yo u r m o n ey an d e a r n a re t u r n o f 5​%. Wha t i s t h e p rese n t v a l u e o f t h e ​ ann u i t y ?

Principal : 4240

Solution steps

Translate the problem into an equation:

10600 = P (1 + 0.05 \cdot 30)

Solve for

P, 10600 = P (1 + 0.05 \cdot 30) : P = 4240

Principal : 4240