Home > #MTBoS, Commentary, Maths, Teaching > Reverse percentages and compound interest

## Reverse percentages and compound interest

The other day a discussion arose in my year 10 class that I found rather interesting. There was a question on interest which incorporated compound interest and reverse percentages. One student was telling the other how to find the answer to the reverse part, “you need to divide it, because it was that amount times by the multiplier to get this amount and divide is the inverse of times.” All good so far, then they discussed how to complete it if it was a reverse of more than one year, “so in that case it’s the new amount dived by the multiplier to the power of how many years.” I was pleased at the discussion so I didn’t really interject.

Then one of them aid, “if I’m looking for two years ago, can’t I just times it by the multiplier to the power -2? Wouldn’t that work.” I thought this was an excellent thought process. The other student disagreed though, sating “no, it has to be divide.” So I thought at this point I’d better interject a little.

“Does it give you the same answer?” I asked. They both thought about it and tried it and discussed it and said yes. So I asked “does it ALWAYS give the same number?” they tried a number of scenarios using different amounts, different interest rates and different numbers of years. Eventually they had convinced themselves. “Yes, yes it is always the same.”

“So is it a valid method then?” I probed. Some more discussion, then one ventured “yes. It must be.”

“Why does it work?”, I then asked. And left them discussing it.

When I came back to the pair I asked if they could explain why it works and one of them said, “we think that it’s because multiplying by a negative power is the same as dividing by the positive version.”

Categories: #MTBoS, Commentary, Maths, Teaching
1. November 15, 2017 at 5:45 pm

Nice. By coincidence I was just doing present value problems last week too.

2. November 27, 2017 at 12:17 pm

Hi Stephen,
I’m following up on my previous message to let you know you have been selected to be featured in “The Best Educational Blogs” list, as selected by our users.
The blog has now been published and can be viewed by following the link below:
https://tutora.co.uk/blog/the-51-must-follow-educational-blogs
Not only has this been shared on the high traffic blog section of the site, but will also be sent out to our userbase of over 60,000 families across the UK.
If you could complete the steps below, this will help us massively promote the blogpost and connect you with a wider audience:
1. Send us a short piece around 100 words about why you love to write about education. This is for us to share with our audience in the emails which will be going out to them to promote the listicle.
2. Add our link to your site. This can be in the form of the best bloggers badge (see attached), a short blogpost or if you have a useful links section add us there.
If you have any questions feel free to drop me a message or give me a call (07900157571).
Looking forward to getting you involved.
Thanks,
Ijaz

1. November 18, 2017 at 4:04 pm