“I read
your columns on APR but I’m not too swift about numbers.
Can you explain it in a way I can understand?”
That’s a challenge because the APR is the
solution of a complicated mathematical equation.
But I’ll give it a try.
Mortgage
shoppers confront the APR as soon as they search for rate quotes, because
under Federal regulations an interest rate quote must also show an APR.
The rationale of this rule is that the APR reflects both upfront
fees and the interest rate, and is therefore a more comprehensive measure
of cost to the borrower than the interest rate alone.
However,
borrowers have difficulty with the concept.
How can you combine into one number interest that is paid every
month over the life of the mortgage, and fees that are paid upfront?
While the
fees are in reality paid upfront, the APR calculation assumes that the
fees are paid over the life of the mortgage in the same manner as the
interest. In the calculation,
the sum of the interest payment in every period and the fees allocated to
that period, as a percent of the balance, equals the APR.
To
illustrate this, I’m going to assume a very simple and unrealistic
mortgage. It is for
$100,000 at 8%, with only 3 annual payments.
Each payment is $38,803.36. Fees
included in the APR are $1,000. The
APR is 8.559%. I solved
for the APR in the conventional way, using a computer.
At the end
of year 1, the interest payment is 8% of $100,000, or $8,000 (see table).
In addition, $559 of the original $1,000 in fees is allocated to
year one. The total of $8,559
is 8.559% of the balance one year earlier.
Similarly,
in each of the next 2 years, the sum of the interest payment and the
upfront fee allocated to that year equals 8.559% of the balance.
It is assumed that until the fees
are allocated, they earn a return equal to the APR.
The original $1,000 plus the$147 interest earned on it over the 3
years just equals the sum of the fees allocated to each year.
