# How do i solve this to find PMT?

I know this may seem like a stupid question but i've been up late working on this math assignment and this question just isn't working when i transpose it.

So this is the formula to find Present Value (PV) and I'm rearranging it to find PMT.

$$PV = PMT - \frac{1-(1 + i/k)^{-n} } {i/k}$$

PV = 429000
K = 12
N = 300
i = 5.11

Can someone link me to an annuity calculator!

• So basically you're trying to find the monthly payment(PMT) of an annuity is it ? – ganeshie8 Aug 20 '14 at 11:53
• is the edit correct? – Vikram Aug 20 '14 at 11:54
• Yes I am trying to find the monthly payment using annuity! – user151764 Aug 20 '14 at 11:56
• You have to use calculator to simplify the expressions, these finance calculations are difficult to carry out without calculator. Are you allowed to use calculator ? – ganeshie8 Aug 20 '14 at 11:57
• Wait I am allowed to use a finance calculator but I need to show my steps of how I got to it. – user151764 Aug 20 '14 at 12:00

## 1 Answer

$PV = PMT\times \left(\dfrac{1-\left(1+\dfrac{i}{k}\right)^{-n}}{\dfrac{i}{k}}\right)$

Your goal is to isolate $PMT$, so simply divide :

$\dfrac{PV}{\left(\dfrac{1-\left(1+\dfrac{i}{k}\right)^{-n}}{\dfrac{i}{k}}\right)} = PMT$

Rearranging a bit you would get :

$\boxed{\dfrac{PV\times \dfrac{i}{k}}{1-\left(1+\dfrac{i}{k}\right)^{-n}} = PMT}$

Plugin the given values and evaluate !

• Thanks man you're the best! – user151764 Aug 20 '14 at 12:57
• you're welcome :) its a good idea to verify your work with wolfram : wolframalpha.com/input/?i=%28429000*%280.0511%2F12%29%29%2F%281-%281%2B0.0511%2F12%29%5E%28-300%29%29 – ganeshie8 Aug 20 '14 at 13:16