#1**0 **

**Please state the payment periods... I will just assume it's annual.**

This is the notation for our problem

PV = A(P/A, i%, n)

Now to set up the formula

PV = A((((1+i)^n)-1)/(i*(1+i)^n)

11000 = 500((((1.005)^n)-1)/(.005*(1.005)^n)

Many methods you could solve for n.

After many guesses I came the value is in between 23 and 24. Furthermore, with linear interpolation I came to the conclusion n=23.4897

Guest Jul 3, 2017

#2**0 **

Guest #1

Note that there is a direct solution for n in this case:

PV=P{[1 + R]^N - 1 / [1 + R]^N} / R

11,000 = 500 x {[1.005]^N - 1 / [1.005]^N} / 0.005

22 ={1.005^N - 1 / 1.005^N} / 0.005

0.11 = {1.005^N -1 / 1.005^N}, solve for N

[200/201]^N = 89/100 take the log of both sides

N = Log[89/100] / Log[200/201]

**N = 23.365**

Guest Jul 3, 2017