Answer to Question #135117 in Financial Math for jaya

Question

The present value of a series of payments of $500 at the beginning of every month years, forever, is equal to $10000. Calculate the nominal annual discount rate compounded monthly.

Answer 1

solution

$payment, \ p = 500$ is paid $monthly\ in \ perpetuity$ and $present\ value ,\ pv =10000$

These represents a series of payments beginning at time 0, i.e annuity in advance

$present\ value =p*\frac{1+i}{i}$

Where $i$ is the monthly compounding rate

$10000 =500*\frac{1+i}{i}$ $20=\frac{1+i}{i}$ $i=\frac{1}{19}=5.2632\%$

Answer

The nominal annual discount rate:

$(5.2632\% )*12=63.1579\%$