Question 1199129: Suppose you want to purchase a $ 195000 house. If you put 20% down and finance the rest in a 15 year mortgage at an interest rate of 4%, what will your monthly payments be?
Monthly payment =
Found 2 solutions by Theo, math_tutor2020:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sale price is 195000
down payment is .20 * 195000 = 39000
finance loan is 195000 - 39000 = 156000
using the financial calculator at https://arachnoid.com/finance/ the payment at the end of each month is equal to 1531.91.
inputs were:
pv = 156000
fv = 0
np = 15 * 12 = 180 months
ir = 4% / 12 = .33333.....% per month
payment is at the end of each month.
output was:
pmt = -1531.91
pv is positive because it's money coming in.
pmt is negative because it's money going out.
the calculator requires those conventions to work properly.
here's what the result from the calculator looks like.
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
20% of $195,000 = 0.20*195000 = 39000
Down payment is $39,000
Remaining amount is 195000-39000 = 156,000
Note that 80% of 195,000 = 156,000
Monthly payment formula
P = (L*i)/( 1 - (1+i)^(-n) )
where,
L = loan amount
i = monthly interest rate in decimal form
n = number of months
We have these input values
L = 156000
i = 0.04/12 = 0.00333333 approximately
n = 15*12 = 180 months
Let's compute the value of P.
P = (L*i)/( 1 - (1+i)^(-n) )
P = (156000*0.00333333)/( 1 - (1+0.00333333)^(-180) )
P = 1153.91285124951
P = 1153.91
Answer: The monthly payment is $1153.91
---------------------------------------------------------
As verification, you can use the calculator the tutor @Theo mentioned.
Keep in mind the answer is 1153.91 and NOT 1531.91; it appears he mixed up the digits.
Another TVM solver is this one here
https://www.geogebra.org/m/mvv2nus2
which emulates the TVM solver in a TI83 and TI84.
The inputs will be:
N = 180
I% = 4
PV = 156000
PMT = left blank or set to whatever you want
FV = 0
P/Y = 12
C/Y = 12
Do not type in dollar signs or commas into any of the boxes.
Here's an explanation of each input:- N represents the number of months in this context
- I% is the annual interest rate as a percentage
- PV is the present value, aka starting loan amount
- FV = 0 to indicate we want the future value of the loan, aka final balance, to be $0 when it's all paid off
- P/Y = 12 means there are 12 payments per year
- C/Y = 12 means there are 12 compoundings per year
After the items are filled into the proper boxes, press the "Solve for PMT" button to have -1153.91 show up in that box.
This value is negative to represent a cash outflow.
|
|
|
