Melody

Yes, it was a strange interpretation - I'll give you that!

(This one is cutesy of Reinout-g)

\begin{array}{|l|l|}32\% & 100\%\\0.32 & 1.00\\43.7 & 136.5625\\\end{array}   

$$\begin{array}{|l|l|}32\% & 100\%\\0.32 & 1.00\\43.7 & 136.5625\\\end{array}$$

Thanks reinout. Is that wolfram|Alpha output suposed to show something?

The quadratic formula, that CPhill used is definitely the way to go.  Why make it hardeer than necessary.

(The other answers are good value too)

This will help you remember it.

If it says BETWEEN -4 and 8 then -4 and 8 should DEFINITELY NOT be included.

You need to give a little more information Carol.

CPhill has guessed what you want and he is most likely correct but what does PMT stand for.  

Not everyone around uses the same letters or acronymes for a particular meaning.

This is obviously a present value question but is it for an ordinary annuity or for an annuity due?

CPhill has assumed ordinary annuity because this is the most common.  

He probably guessed correctly.

Thanks Chris.

now I need to work out what Diane's new repayments will be if her interest rate drops to 4%

30 years is remaining on the loan.

This is the present value of an ordinary anuity so you will use this formula (same formula)

$$A=R\times \frac{1-(1+i)^{-n}}{i}$$

A=285308.73

R=$??

i=4%/12=0.3repeater%=0.003333333....

n=30*12=360 months

$$\begin{array}{rll}
285\;308.73&=& R\times \frac{1-(1.00\dot3)^{-360}}{0.00\dot3}\\\\
285\;308.73&=& R\times 209.4612296\\\\
R&=&\$ 1362.11 \mbox{ to the nearest cent}
\end{array}$$

------------------------------------------------------------

So her payments dropped from $1710.57 to $1362.11

$${\mathtt{1\,710.57}}{\mathtt{\,-\,}}{\mathtt{1\,362.11}} = {\mathtt{348.46}}$$

This would save Diane $348.46

------------------------------------------------------------

Now all of this is assuming that I have made no careless mistakes.

At least the numbers pass the sensibleness test (I think)

Now, please tell me if you have the answer in the back of a book or somewhere.

NOW you will need to work out the present (5years down the track) value of the loan

This is the present value of an ordinary anuity so you will use this formula (same formula)

$$A=R\times \frac{1-(1+i)^{-n}}{i}$$

A=??

R=$1710.57

i=6%/12=0.5%=0.005

n=30*12=360 months

$$\begin{array}{rll}
A&=& \$ 1710.57\times \frac{1-(1.005)^{-360}}{0.005}\\\\
A&=& \$ 1710.57\times 166.79161444\\\\
A&=&\$ 285\;308.73 \mbox{ to the nearest cent}
\end{array}$$

------------------------------------------------------------

So after 5 years Dianne owes the bank $285 308.73

I am going to answer this in a series of posts because it is long and I am going to have to do some homework along the way

FIRST

first you will need to find the initial repayments.

This is the present value of an ordinary anuity so you will use this formula

$$A=R\times \frac{1-(1+i)^{-n}}{i}$$

A=300000

i=6%/12=0.5%=0.005

n=35*12=420

$$\begin{array}{rll}
300000&=& R\times \frac{1-(1.005)^{-420}}{0.005}\\\\
300000&=& R\times 175.3802262\\\\
R&=&\$ 1710.57 \mbox{ to the nearest cent}
\end{array}$$

Okay now I have to work out how to find the amount that will still be owing after 5 years.