Simple average for poor tradesman

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Hello people. I'm an 30 something tradesman with a math problem. It relates to my mortgage and my desire to learn. I want to know know how to average two term interests. First rate-4.29 for 9 mnths , second rate 5.3 for 51 months. What is the average rate over the full 60 mnth term. Thank you for any help and if you could please show work.
 
Are these two different loans...? Are they simple interest, or compound? If compound, what is the compounding interval? What formulas does your book give you to use?

When you reply, please show your work. Thank you.

Eliz.
 
Hello, blackglory75!

Hello people. I'm a 30-something tradesman with a math problem.
It relates to my mortgage and my desire to learn.
I want to know know how to average two term interests.
First rate: 4.29% for 9 months; second rate: 5.3% for 51 months.
What is the average rate over the full 60-month term.
Click to expand...
You say it's a <u>mortgage</u> . . . hence, you're making monthly payments.
\(\displaystyle \;\;\)Without more information, we can't answer your question.

If this were a straight loan (simple interest), we could work out an average rate.

For example: $1000 for 5 years with an variable interest rate.
\(\displaystyle \;\;\)For the first 9 months, the interest is: \(\displaystyle \$1000\,\times\,0.429\,\times\,\frac{3}{4}\:=\:\$32.175\)
\(\displaystyle \;\;\)For the remaining \(\displaystyle 4\frac{1}{4}\) years, the interest is: \(\displaystyle \$1000\,\times 0.052\,\times\,4.25\:=\;\$225.25\)
Hence, you are charged \(\displaystyle \$257.425\) interest over the 5 years.

This is a rate of \(\displaystyle \frac{257.425}{1000} = 0.257425\) for the 5 years

\(\displaystyle \;\;\) or: \(\displaystyle \frac{0.257425}{5}\,=\,0.051475\,\approx\,5.15\%\) per year.

And that's the best I can do . . .
 
blackglory75 said:
Hello people. I'm an 30 something tradesman with a math problem. It relates to my mortgage and my desire to learn. I want to know know how to average two term interests. First rate-4.29 for 9 mnths , second rate 5.3 for 51 months. What is the average rate over the full 60 mnth term. Thank you for any help and if you could please show work.
Click to expand...

First, I presume you presently have a mortgage at 4.29%, and your mortgage
still has 9 months to go at that rate; then, the rate will be re-negociated at some
rate which is now unknown; that rate is now 5.3%; you want to play safe (in case
rate is higher than 5.3% in 9 months) and therefore decided to "contract" for
this 5.3% now, but of course want to continue the lower 4.29% for 9 months:
so a new mortgate agreement NOW for 60 months will be arranged at a rate that
reflects 4.29% for the first 9 months, then 5.3% for the remaining 51 months.
(This is done routinely up here in Canada)

If that's the case, I suggest you first find out from the lender if it possible to be
guaranteed NOW that the 5.3% will be the maximum rate in 9 months; it's sure
worth the try; if so then you have no problems...and could possibly renegociate
at a lower rate than 5.3% in 9 months.

If not, the average rate (known as blended rate up here) you're trying to
calculate depends (as Soroban points out) on the amount owing or borrowed;
in your case, is it a brand new mortgage?
 
Mortgage rate average

Thank you all very much. I apologize for not being more concise in my description of the problem. Soroban your respnose gave me the answer and cleared it up quite nicely thank you. Have a nice day and Happy New Year all.
 
So then that means you were simply looking for a simple average,
regardless of a mortgage or not.

You can set up any M months scenario at rates A and B, rate A being for first F months:

average rate = [F*A + (M-F)*B] / M

your example: [9*4.29 + (60-9)*5.3] / 60 = 5.1485
 
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