I have an unusual statistical question to ask...

Question

I would like to calculate a percentage increase per incremental period. For example, let's say that the national debt increased from $100 billion to $150 billion (wishful thinking) during a president's two terms in office. Over-all, that's an increase of 50% from where it started, but HOW WOULD I CALCULATE THE PERCENTAGE THAT THE DEBT INCREASED PER TERM? Assuming that the rate of increase was equal in each term, it would obviously be less than 25% per term, because that would yield $162.5 billion and would not account for the compounding influence. If you can spare the time I would appreciate the formula (if indeed there is one). Cheers, SG

Answer 1

FV = $150B

PV = $100B

r is interest rate. 

 

After eight years FV = PV(1+r)^8  (eight years is two terms)

To solve take the log of both sides

 

log(FV) = log(PV) + 8log(1+r). sove for (1+r)

 

(log(FV) - log(PV))/8 = 1+r Take the logs divide by 8 and solve for r

Answer 2

There is indeed a basic formula:  

 

FV=PV(1+r)^t

 

FV = future value

PV = present value

r = rate

t = time

 

In this case, t = 2 (for rate per term), FV = 150, PV = 100, can you solve for r?

 

r = ((150/100) ^0.5) - 1 = 0.224744871

 

That is, $100 billion increased by approximately 22.5% per term.

 

-Cheers