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October 2, 2014

October 2, 2014

Posted by **Gabby** on Friday, March 15, 2013 at 11:04am.

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 -
**Ms. Sue**, Friday, March 15, 2013 at 11:14amThe amount you've borrowed is your principal.

- Economics -
**Reiny**, Friday, March 15, 2013 at 11:18amIn 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 -
**Reiny**, Friday, March 15, 2013 at 11:23amshould 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 -
**Gabby**, Friday, March 15, 2013 at 11:43amI 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 dont understand your method - can you explain in laymen terms

- Economics -
**Reiny**, Friday, March 15, 2013 at 1:30pmPrecisely 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 -
**Gabby**, Friday, March 15, 2013 at 2:20pmI am still confused. Is this wrong?

- Economics -
**Reiny**, Friday, March 15, 2013 at 3:00pmIs what wrong?

- to be confused ? or

- my answer ? or

- your answer ?

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

payment is steady at 1727.99

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 -
**Gabby**, Monday, March 18, 2013 at 9:14amI 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 -
**Gabby**, Monday, March 18, 2013 at 11:23amI 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?

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