Suppose I borrow $10, to be repaid as a lump sum after five years, with one dollar interest to be paid annually.
|Year 0||Borrow $10|
|Year 1||Pay Interest $1|
|Year 2||Pay Interest $1|
|Year 3||Pay Interest $1|
|Year 4||Pay Interest $1|
|Year 5||Pay Interest $1 Principal $10|
I pay back a total of $15 for $10 borrowed.
The graphs I've shown recently, comparing "nominal" to "real" Federal debt to GDP ratios, consider only the principal amounts. Not the interest. Now I want to consider the interest payments as well as principal.
Specifically, I want to see how well interest payments fill the gap between nominal and real on my graphs. Does interest make up the shortfall created by inflation? Does it more than make up for the shortfall? Or does a shortfall remain?
Suppose I borrow $10, to be repaid after five years pass, with one dollar of interest paid annually, and with inflation that reduces the dollar's value by ten cents each year. The "real" value of the dollar would be:
|Year 1:||90 cents|
|Year 2:||80 cents|
|Year 3:||70 cents|
|Year 4:||60 cents|
|Year 5:||50 cents|
In year zero, when a dollar was worth $1.00, I borrowed $10. I received the value $10.
In year one, when a dollar was worth 90 cents, I paid $1 interest. I paid a year-zero value equal to 90 cents.
In year two, when a dollar was worth 80 cents, I paid $1 interest. I paid a year-zero value equal to 80 cents. The lender has received from me a total of $1.70 of year-zero value. Here, I don't need to type it all out:
Oh look at that. Open Office doesn't like the way I shortened the word accumulation.
So in this example, the lender is repaid $8.50 out of $10 "real" value dollars. A better way to say it may be that, when we consider principal and interest and inflation, the lender received back 85% of the value lent out.
All of this of course assumes that it is reasonable to expect to be repaid at equal value rather than an equal number of dollars. In an inflationary world, that assumption may not be reasonable.