Hey! (:
I have attempted this question but I dont have answers and I am pretty sure it is not correct, if it isn't, can you please show me how to do it?
Terry borrowed $20000 on 1 January 2008. He agreed that on 1 January in each succeeding year he would pay back $3000 and add 6%p.a. interest on the amount owing during the year just completed. Find:
a) the amount still owing after ! January 2013
b) the number of years needed to pay off the debt
My answers: a) $22181.51 b) 120.7 years
Hey! Yeah not quite, but that's all good, let me show you!
So we start with $20,000, let that be \(A_0\). After 1 year (so, January 2009), we add 6% interest and then pay back $3000. That looks like this:
The next year, we take
that amount, and do the same thing. Add 6%, subtract $3000:
If you expand, you'll get what I've got above! And if you do it again, you should get:
See the pattern? If you're just starting this topic it might look strange, but do a few of these and this is what they all look like, more or less. After 5 years (2013), we have:
Pop that in your calculator, I get $9853.23!! For Part (b), you need to instead consider a general version of the expression, after \(n\) years:
We need \(A_n=0\) -> See if you can manipulate that expression to find \(n\)! If you've never done a question like this before let me know and I'd be happy to show you, or perhaps read
this guide which steps through it for you! Happy to help if anything above was confusing as well - I'm assuming you've seen something similar to it before but can definitely go slower if you haven't