# Math Help - Calculating percentage paid on debt post inflation.

1. ## Calculating percentage paid on debt post inflation.

I'll start by presenting it as a hypothetical problem:
After studying for 3 years at university I have student debt of 65224. My interest rate is 3.15%, inflation is assumed to be 3% each year so the above inflation interest is 0.15%, I pay back 90 a year (let's call these payments deductions) and we assume that the payments rise with the rate of inflation. After 30 years, any remaining debt is wiped.
What is the best way to work out, after 30 years, what percentage of my original debt I have paid in inflation interest, above inflation interest, and deductions?
I have my own way of doing it but it is extremely long winded so I don't think it's the best way.
then inflation = 1957,
then deductions from debt = 65224 - (90*1.03) = 65131,
I then repeat the process starting with 65131,
Meanwhile I have a separate tally of what the above figures are after 30 years of inflation,
so I'll multiply each of the above figures by 1.03^remaining years of inflation.
I'll then sum up these inflated figures and divide the sum by 65224*(1.03^30) to see what each element added up to as a percentage of the original debt post inflation.

It's based on some optimistic assumptions, I know but I'm just trying to get an idea. I hope it all makes sense too.

2. ## Re: Calculating percentage paid on debt post inflation.

Originally Posted by sheldonisgod
I hope it all makes sense too.
Not to me...but don't let that bother you!

For your info: $65,224 over 30 years at annual rate of 3.15% requires annual payment of$3,392.53

3. ## Re: Calculating percentage paid on debt post inflation.

I should have clarified how what I call my annual deductions do not include the interest payments, so the inflationary interest payments make up the bulk of my payments to this debt. Also, as a rule in the UK, any student debt that remains, 30 years after graduation, does not have to be paid, its the governments problem from then on.
The way I looked at it was inflation interest charged (Retail Price Index) goes towards lowering the debt even though you do not see how it directly lowers the debt, as the debt remains the same after interest is charged. This is because as inflation occurs, the debt you owe would increase but the value of the debt would remain the same, so when you pay for inflation you're only paying for the difference between pre-inflation and post-inflation debt. When you pay interest on inflation, your debt remains as the same figure but has actually reduced in value because that figure has less buying power.

In my example, I also make the assumption that my wages increase with the rate of inflation, so therefore I decide to increase my deductions to the debt at the rate of inflation too, but in effect, the deductions are of the same value each year.

I also need to know what these figures translate to after 30 years of inflation so I can see what the annual interest payments added up to as percentage of the original debt (by debt I don't include what I have also been charged in above inflation interest, the 0.15%). Because each payment will have already been subject to x years of inflation, I need to adjust my treatment of the payment accordingly: payment*(1.03^30-x)= what payment figure looks like after 30 years.
Hope that helps!

4. ## Re: Calculating percentage paid on debt post inflation.

I should have clarified how what I call my annual deductions do not include the interest payments, so the inflationary interest payments make up the bulk of my payments to this debt. Also, as a rule in the UK, any student debt that remains, 30 years after graduation, does not have to be paid, its the governments problem from then on.
The way I looked at it was inflation interest charged (Retail Price Index) goes towards lowering the debt even though you do not see how it directly lowers the debt, as the debt remains the same after interest is charged. This is because as inflation occurs, the debt you owe would increase but the value of the debt would remain the same, so when you pay for inflation you're only paying for the difference between pre-inflation and post-inflation debt. When you pay interest on inflation, your debt remains as the same figure but has actually reduced in value because that figure has less buying power.

In my example, I also make the assumption that my wages increase with the rate of inflation, so therefore I decide to increase my deductions to the debt at the rate of inflation too, but in effect, the deductions are of the same value each year.

I also need to know what these figures translate to after 30 years of inflation so I can see what the annual interest payments added up to as percentage of the original debt (by debt I don't include what I have also been charged in above inflation interest, the 0.15%). Because each payment will have already been subject to x years of inflation, I need to adjust my treatment of the payment accordingly: payment*(1.03^30-x)= what payment figure looks like after 30 years.
Hope that helps!

5. ## Re: Calculating percentage paid on debt post inflation.

I'm more confused than I was!

.0015 * 65225 = 97.84 (~8 per month!) , so why worry about such a meaningless amount
when "estimating" over a 30year period...

Interesting reading (almost a joke!) here:
Student loans in the United Kingdom - Wikipedia, the free encyclopedia

Hope someone else here can take a few Tylenols and help you...

6. ## Re: Calculating percentage paid on debt post inflation.

Basically, what's happened here in the UK, is new students (me) commencing study in 2012 now have to pay above inflation interest rates whereas before there was no added cost in taking out a loan. With salary after graduation, for every £1 you earn above 21,000, you have to pay 0.00015% on above inflation interest up until your salary exceeds 41,000 where the above inflation interest remains at 3% as the above inflation interest stops increasing for every £1 you earn above 41,000 in your salary.
I'm trying to build a case to show why this system is more extortionate than it looks. So far, I've applied my method to a case where I earn 40K a year and have found that I pay back 132% of the original debt where 32% has to gone to above inflation interest. It's also unfair how the more you earn above 41K, the less you have to bay pack on above inflation interest.
I'm looking for formulas to make the calculation process quicker so I can try more sophisticated examples with ease such as how much more the lowest earners pay back on the principle and above inflation interest when the wages lag exponentially behind the rate of inflation (which they do).

7. ## Re: Calculating percentage paid on debt post inflation.

if you want to look at how expensive the debt is, in a way that is comparable to other forms of debt, you could start by calculating a schedule of payments and then the AER.

ill resist the temptation to comment on what you perceive as fair, since thats politics and this is a maths forum.

8. ## Re: Calculating percentage paid on debt post inflation.

Could you explain to me in more detail what I have to do and what AER is please?
Thanks

9. ## Re: Calculating percentage paid on debt post inflation.

Originally Posted by sheldonisgod
Could you explain to me what AER is please?

10. ## Re: Calculating percentage paid on debt post inflation.

I don't know whether that was an insult to my ignorance or you have really poor humor. Either way I've reported you as punishment haha.

11. ## Re: Calculating percentage paid on debt post inflation.

Assumed you could "take a joke"....more so after seeing sheldonISGOD !

Don't know what "insult to my ignorance" means...anyhow, pretty hard
for me to know HOW to insult...since I don't know you from Adam...