Problem Solving

A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $320,000, 80% of which was in the first mortgage, what is her APPROXIMATE monthly interest payment?

A) $1,333
B) $1,733
C) $3,466
D) $13,333
E) $20,796

Another approach is to use some ESTIMATION and NUMBER SENSE.

Given:
80% of $320,000 at 4% interest rate
20% of $320,000 at 9% interest rate

Since MOST (80%) of the mortgage is at 4% interest rate, let's see what would happen if 100% of the $320,000 mortgage was at the 4% interest rate.
To make it easier to calculate, let's round the mortgage down to $300,000

4% of $300,000 = $12,000, so this is the ANNUAL interest payment.
This translates into $1000/month.
Now if we had factored in the fact that 20% of the mortgage is charged 9% interest AND the fact that we should have used $320,000 (rather than $300,000), what effect would this have on the $1000/month interest payment?

If we have a strong number sense, we will have a general feeling that the interest payment is a BIT BIGGER than $1000/month.

So, choose A

Cheers,
Brent

A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $320,000, 80% of which was in the first mortgage, what is her APPROXIMATE monthly interest payment?

A) $1,333
B) $1,733
C) $3,466
D) $13,333
E) $20,796

Here's another approach that uses some ESTIMATION and NUMBER SENSE.

Given:
80% of $320,000 at 4% interest rate
20% of $320,000 at 9% interest rate

Let's examine what would happen if HALF of the $320,000 were charged 4% interest, and HALF were charged 9% interest.

The result would be a COMBINED annual interest rate of 6.5%.
Now what is 6.5% of $320,000?
Hmmm, that's too much work.
Let's calculate 6% of $300,000 instead. This works out to ANNUAL interest payment of $18,000, which translates into $1500/month
So, using some NUMBER SENSE, we can conclude that 6.5% of $320,000 results in interest payments in the range of $1700-$1800/month

Of course, this is the resulting payments when HALF of the $320,000 are charged 4% interest, and HALF are charged 9% interest.
In actuality, 80% is at 4% and only 20% is at 9%. So, the monthly payments will be a fair bit LESS THAN $1700-$1800

So, choose A

Cheers,
Brent