# Economics

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%?

1. 👍 0
2. 👎 0
3. 👁 54
1. The amount you've borrowed is your principal.

1. 👍 0
2. 👎 0
2. 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

1. 👍 0
2. 👎 0
posted by Reiny
3. 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

1. 👍 0
2. 👎 0
posted by Reiny
4. 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

1. 👍 0
2. 👎 0
posted by Gabby
5. 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. )

1. 👍 0
2. 👎 0
posted by Reiny
6. I am still confused. Is this wrong?

1. 👍 0
2. 👎 0
posted by Gabby
7. 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.

1. 👍 0
2. 👎 0
posted by Reiny
8. 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?

1. 👍 0
2. 👎 0
posted by Gabby
9. 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?

1. 👍 0
2. 👎 0
posted by Gabby

## Similar Questions

1. ### Math.

For question 1-4 for the interest. All rates are annual interest rates. 1) principal, \$400 rate, 5% time, 1 year. a. \$10 b. \$20 c. \$40 d. \$200 2) principal, \$1,000 rate, 8.5% time, 3 years a. \$255 b. \$170 c. \$22.5 d. \$17 3)

asked by Sydney HELP! Need help ASAP! on April 9, 2015

*principle or principal(do these make sense?) -She was a person of strong PRINCIPAL. -The PRICIPALS sat together at the district confrence. -How much of the total in my savings account is PRINCIPAL? -His hay fever was the

asked by astasia on April 16, 2010

Information which comes to the knowledge of an agent is: a) required to be communicated to the principal in all circumstances. b)is imputed to the principal. c) can be disclosed to the principal only with the third party's

asked by Sue on April 10, 2007
4. ### Consumer Math

*** is my answer When calculating intrest on a cd you ____? A. multiply the principal by the intrest rate B. multiply the principal by the intrest rate and time*** C. use an online calculator D. multiply the principal by time

asked by Kamryn on November 21, 2017
5. ### math

An investor purchases 75 shares at 37.90 a share, holds the stock for 150 days, and then sells the stock for 41.20 a share. Find the annual interest rate earned. principal under 3000 3000-10,000 over 10,000 commission 32+1.8% of

asked by Tiffany on March 1, 2013
6. ### math

The buying and selling commission schedule shown below is from a well-known online discount brokerage firm.? Taking into consideration the buying and selling commissions in the schedule find annual rate of interest earned by each

asked by b on May 2, 2013
7. ### math

Does anyone know how to find the rate with ONLY principal and time? (no interest) Refer to this: Investment A: Rate as 'R,' principal as \$8000, time as '4 years,' and interest as 'SI'

asked by Anonymous on November 17, 2017
8. ### algebra

A principal of \$5000 was invested in a savings account for 4 years. If the interest earned for the period was \$400, what was the interest rate? i know this is 1.5 % or at least I think it is but how do i write it out? Use the

asked by confused on May 30, 2007
9. ### math

The amount of money in an account with continuously compounded interest is given by the formula A = Pert, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the hundredth of a year

asked by Greg on April 22, 2007
10. ### Pre-calc

HI, can someone can please help me find the coordinates of the two halfway points of the principal cycles. Here are some answers that might help. -I found the interval: (0,pi/2) -The equation of the left vertical asymptote: x=0,

asked by chizoba on August 9, 2016

More Similar Questions