SOLUTION: I have been really stuck on this problem for a while.
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Suppose your parents want to buy a house for $200,000. They have $2
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Question 992738: I have been really stuck on this problem for a while.
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Suppose your parents want to buy a house for $200,000. They have $20,000 for a down payment.Their mortgage will have an annual interest rate of 6%. The loan is to be repaid over a 30-year period.
a. How much will your parents have to borrow?
b.How many monthly payments would there be?
c.What will the monthly payment be?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Suppose your parents want to buy a house for $200,000. They have $20,000 for a down payment.Their mortgage will have an annual interest rate of 6%. The loan is to be repaid over a 30-year period.
a. How much will your parents have to borrow?
the house costs 200,000.
they put 20,000 down.
their mortgage will be 200,000 - 20,000 = 180,000
b.How many monthly payments would there be?
the loan is to be repaid over a 30 year period.
they will be making monthly payments.
the number of monthly payments will be 30 * 12 = 360
c.What will the monthly payment be?
this is the hard one.
if you have a financial calculator, it becomes easy enough.
if you need to use a formula, then you have to have access to the right formula to use.
the first thing you need to do is convert the annual percentage to a monthly percentage by dividing it by 12.
6% / 12 = .5% per momth.
if the calculator asks for percent, then you enter .5 as the percent.
if you use a formula, you will need to convert the percent to a rate.
.5% divided by 100 = .005.
here's a calculator you can use that makes the job easy.
http://www.arachnoid.com/lutusp/finance.html
here's a picture of my inputs from your problem and the answer that the calculator gave me.
the monthly payment is 1709.19
if you enter the mortgage amount as a positive number, it will tell you the payments as a negative number, and vice versa.
payments at the end of each month are assumed unless otherwise indicated by the problem.
ther calculator default should be end of month.
if end of month is not already selected, then select it.
a simplified version of the formula is shown below:
pmt = (r * (pv * (r+1)^n) / ((r+1)^n -1)
r is the monthly interest rate (not percent).
it is equal to .005 which is the monthly percent divided by 100.
n is the number of time periods which is the number of months which is equal to the number of years * 12 which is equal to 30 * 12 = 360.
pv is the present value of the loan which is equal to the price of the home minus the down payment which is equal to 200,000 minus 20,00 = 180,000.
commas are for clarity.
don't use them in the formula.
replace r and n and pv with their appropriate values and the formula becomes:
pmt = (.005 * 180000 * 1.005^360) / (1.005^360 - 1)
do the math and the answer you get will be:
pmt = 1079.190945
key points:
mortage = price of home minus down payment.
number of months = number of years * 12
percent per month = percent per year / 12
interest rate = percent / 100
in the formula:
n is the number of time periods
r is the interest rate per time period
pmt is the payment per time period
time period is months
payments are assumed to be end of time period payments
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