Question 1182345: (Amortization) A store was purchased for P725,000 and the buyer made a 10% down payment. The balance was financed with a 6.35% loan for 27 years. Find the monthly payment.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Here is the form of the formula for calculating a loan payment that I use:
P is the principal -- the amount of the loan
A is the monthly payment
i is the annual interest rate
n is the number of compounding periods per year
t is the number of years
Note those definitions make i/n the periodic interest rate (annual interest rate divided by number of periods per year) and nt the total number of payments (number of years times number of periods per year).
For your example....
To find the amount of the loan payment A, evaluate the expression in parentheses and divide the loan amount 652500 by the result.
To evaluate the expression in parentheses, you will need a calculator. Perform the calculation in small steps; trying to evaluate the whole expression at once can easily result in misplaced parentheses, resulting in absurd loan amounts like $3.21 or $2,594,039.55.
(1) calculate i/n
(2) add the 1
(3) raise the result to the (-12*27) power
(4) subtract the result from 1
(5) divide the result by i/n
Dividing the amount of the loan by this number gives the amount of the payment. That means this number is the number of payments you would need to make to pay off the loan if there were no interest.
On a typical loan, the total amount you pay including interest amounts to about double the original loan amount. So the actual number of payments should be about twice this number.
So if you want to check the calculations you have made to this point, verify that this number is about half the number of payments. Since in this example the number of payments is 12*27=324, the number you have for the whole expression in parentheses should be about 324/2=162. If it's not, there was something wrong in your calculations.
And of course if your number at this point is something close to 162, then you are probably okay, the loan amount is the original amount of the loan, divided by this number.
You should come out with a loan payment of $4215.22 to the nearest cent.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Regarding the long formulas in the post by @greenestamps, I'd like to give couple advises to you.
First, I am 100% sure that for such calculations, your teacher allows you to use a modern Technology.
For such calculations, I usually use MS Excel in my computer.
It is enough for you to copy the entire formula into the cell of the MS Excel spreadsheet, and you will get the number in one click.
Otherwise, if you do not have MS Excel or some equivalent software in your comp,
you may use appropriate online calculators.
One such popular online calculator you may find at this web-site
www.desmos.com
Again, you copy-paste the entire formula into the specialized window of this calculator and get the answer in one click.
This service is free of charge.
Surely, the formulas that you copy-paste, must be written CORRECTLY - it is YOUR RESPONSIBILITY.
I think that to calculate so long formulas using the pocket calculator is
a) a kind of torture,
and
b) an infinite source of errors.
In the XXI century nobody calculates this way.
Hope my advises will be useful for you.
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