Question

does anybody know how to calculate fixed rate mortgages?

Answer 1

What's the specific question your teacher is asking?

Answer 2

So for my assignment I have to find a house and calculate my adjustable rate mortgage. She said I had to re-do it, so I was wondering how to calculate the ARM 3% with terms 5/1 with a 2/6 cap for 30 years? I know it's a long question but I just don't really want to re-do it.

Answer 3

\(\color{#0cbb34}{\text{Originally Posted by}}\) @biancajhernan
So for my assignment I have to find a house and calculate my adjustable rate mortgage. She said I had to re-do it, so I was wondering how to calculate the ARM 3% with terms 5/1 with a 2/6 cap for 30 years? I know it's a long question but I just don't really want to re-do it.
\(\color{#0cbb34}{\text{End of Quote}}\)
well if your teacher tells you to re-do it, then do it to make a better grade. I'm not telling you what to do, just telling you the best option.

Answer 4

I just need help how to calculate it, that's all.

Answer 5

i can help you with that

Answer 6

Thank you, Samantha :)

Answer 7

So to start things off, the "\(\color{red}{5}\)/\(\color{blue}{1}\)" means that the interest rate is fixed at 3% for the first \(\color{red}{5}\) years. After that point, the interest rate will go up by some percentage point every \(\color{blue}{1}\) year.

After this fixed rate period (5 years) is over, the interest rate will go up according to the "\(\color{green}{2}\)/\(\color{orange}{6}\) cap" notation. Specifically, it will increase by \(\color{green}{2}\) percentage points each year until it caps out at \(\color{orange}{6}\)%. The cap is there to ensure that the interest rate doesn't just eat the entire payment (or else you'll never be able to pay off the house and you'll be making 100% interest payments only)


So we have
year1 = 3%
year2 = 3%
year3 = 3%
year4 = 3%
year5 = 3%
year6 = 5% ..... the first year the interest rate goes up
year7 = 6% ..... we go up another 2 percentage points, and hit the cap

Everything after year 7 will stay at 6% interest

Answer 8

Thank you so much I appreciate it.

Answer 9

Now as for the monthly payment, that gets a bit trickier.

The formula we use is
\(\large P = L*\frac{c*(1+c)^n}{(1+c)^n-1}\)
Where,
P = monthly payment
L = loan amount
c = monthly interest rate in decimal form
n = number of months

The value of L is the home value minus whatever the down payment you made. Any other fees are tacked onto the down payment. Usually the down payment is about 20% of the home's value, meaning you are loaned 80% of the home's value.

Eg: if the house is worth $100,000 then you'll make a $20,000 down payment, and be loaned $80,000. So L = 80000 would be used. But you'll likely use a different L value for whatever home you find.

The entire mortgage is over 30 years, which is equivalent to n = 30*12 = 360 months
We also would say
c = (annual rate)/12
c = 0.03/12
c = 0.0025

If we used L = 80000, then we would have this as the monthly payment for the first five years
\(\large P = L*\frac{c*(1+c)^n}{(1+c)^n-1}\)

\(\large P = 80000*\frac{0.0025*(1+0.0025)^{360}}{(1+0.0025)^{360}-1}\)

\(\large P \approx 337.283226983564\)

\(\large P \approx 337.28\)

The monthly payment would be $337.28 for those first five years. The monthly payment would increase after year 5 due to the interest rate increasing.

Keep in mind that this is an example based on a $100,000 home value. The value of L would be different for some other different home value.

Answer 10

After those 5 years are up, the remaining balance on the loan is then used as the new L value, and n is adjusted to n = 25*12 = 300 to account for the fact that you are paying off this new balance over the timespan of 25 years (instead of 30). This recalculation of the payment is done every time the interest rate changes. This is why ARMs can be a pain when it comes to keeping track.

Answer 11

Oh and I nearly forgot, but c is recalculated as well

Eg: if the annual rate becomes 5%, then
c = 0.05/12 = 0.004167 approximately

Answer 12

Thank you!!

Answer 13

You're welcome