# Economics

posted by on .

How do I figure out the principal in the equation principal X rate X time?
I am borrowing \$255,920.00 which is the total amount of the home (\$319,900.00) minus \$63,980.00 (20%I put down).
I am trying to figure out what my monthly payment on the loan which willneed to be paid back in 25 years at 6.5%?

• Economics - ,

The amount you've borrowed is your principal.

• Economics - ,

In this day and age , simple interest just wouldn't be used for a payment plan spanning 25 years, every institution of lending would use compound interest.
(unless you are borrowing from grandpa, who probably wouldn't charge you any interrest)

Here is what is done in reality:

let the payment be P
Balance owing = 319900 - 63980 = 255920
monthly rate = .065/12 = .00541666.. (store in calculator memory)
n= 12(25) = 300

Using the compound interest formula

present value = payment ( (1+i)^n - 1)/i

255920 = P ( (1+.005416667)^300 - 1)/.005416667
255920 = P(748.8364316
P = 255920/748.8364316 = \$ 341.76

• CORRECTION - Economics - ,

should have realized my payment was waaayyy too low.
formula is
PV = Payment (1- (1+i)^-n)/i

255920 = P (1 - 1.005416667^-300)/.0054166667
255920 = P(148.1027056)
P = 255920/148.1027056
= \$ 1727.99

• Economics - ,

I got a different answer -
My calculations show
\$255,920.00(Principal) X 0.065 (Rate of 6.5%) X 25 (Time-25 years) = \$415,870.00
415,870.00 + \$255,920.00 = \$671,790.00
\$671,790.00 divided by 300 months

Monthly payment of 2,239.30
Reiny I don't understand your method - can you explain in laymen terms

• Economics - ,

Precisely my point.
There are two main methods to calculate interest
1. simple interest method - used for short periods of time, usually less than a year
2. compound interest - used in today's financial calculations

you used the simple interest method.
the interest in the first year is approximately equal to what you get if you find
225920 x .065 x 1 = \$14, 684.80
you multiplied that by 25 for a total of appr 415,000
But, ...... as you pay off the loan , the balance is declining, so the interest that you are charged each month (or year) would also be declining.
Your 415,000 interest would include an interest charge of \$14,684 for even the last year. Clearly with only a year to go, you would have a balance of only a few thousand dollars owing.
Your calculations would be roughly 10% interest rate compounded monthly

( On the other hand , if you want me to loan you the 255,920 and pay me \$2,239.30 a month for the next 25 years, I will gladly oblige. )

• Economics - ,

I am still confused. Is this wrong?

• Economics - ,

Is what wrong?
- to be confused ? or

There is no right or wrong answer.
It depends on the method of calculation that is defined
I am extremely doubtful that a lending institution such as a bank would use any other method than the compound interest method I used.

If you are familiar with a spreadsheet such as Excel
you can actually set up a table which shows the gradual decrease in your debt. That is called an amortization table.

Here would be the first three lines

Time - interest- payment - reduction of balance - balance

0 ----- 0------0 ---------0 ------------- 255920.00
1 - 1386.23 -- 1727.99 --341.76 -----------255578.24
2 - 1384.38 -- 1727.99 --343.61 -----------255234.63
etc

where interest = balance of previous month x .00541666667
reduction of balance = 1727.99 - interest
balance = previous balance - reduction in balance.

at time = 300 you should have a balance of appr \$0
You might be out a few pennies due to roundoff error

Even for the first few entries you will notice that the interest each month is slightly less than the previous one, making your reduction slightly more each time.
at the beginning of your mortgage, the payment is made up of mostly interest, but near the end the reverse will be true.

• Economics - ,

I am confused and I understand that thereis no wrong or right answer. The question I need answered is At the end of 25 years, (300 payments) how much will I have paid for my mortgage?

• Economics - ,

I am confused and I understand that thereis no wrong or right answer. The question I need answered is At the end of 25 years, (300 payments) how much will I have paid for my mortgage?