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:

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