Expert: Abe Mantell - 5/26/2009

Question
Hello:

How would most mathematicians solve the following:

Determine the annual interest rate on $1,200 for 6 months, if the interest amount paid is $24?

The following calculation seems to be popular: $24/($1,200 X 6/12), but what is the most common method used?

Should $1,200 be multiplied by 6/12 and then divide $24 by $600 ($600 earns $24 every six months), or should $24 be multiplied by the inverting 6/12?

I thank you for your reply.

Answer
Hello Kenneth,

Depends on if the interest is compounded or simple, and if compounded
then how often?  Do you know?

The formula for simple interest (i.e. not compounded) is:
A=P*(1+r*t),
where P=the principle (i.e. initial amount), A=final value/amount
r=APR (in decimal form)
t=# of years

If we use this, then we would have
1200+24=1200(1+r*0.5) ==> 1224=1200(1+0.5r) ==> 1224/1200=1+0.5r
==> 0.5r=1.02-1 ==> r=0.04 or 4%
Which is equivalent to your "$1,200 be multiplied by 6/12 and then divide $24 by $600 ($600 earns $24 every six months)"

In real life though, most problems like this involve compound interest.
In which case, the formula is:
A=P*(1+r/n)^(n*t)...then things get a bit more complicated to solve.

I hope this helps.

Abe