Question 1181754: You want to buy a $250,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan at 5.35% interest for the rest. What will your monthly payments be? How much of the first payment is interest?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Home value = $250,000
20% of home value = 0.20*($250,000) = $50,000
Down Payment = $50,000
The loan amount is the difference of the home value and the down payment
250,000 - 50,000 = 200,000
So the bank will loan you $200,000
This is the amount you have to pay back (aka principal) and you'll pay interest on top of that.
To find the monthly payment, we'll use this formula
P = (L*i)/( 1-(1+i)^(-n) )
where in this case,
L = 200,000 = loan amount
i = r/12 = 0.0535/12 = 0.00445833333333333 approximately
n = 12y = 12*30 = 360 months
So,
P = (L*i)/( 1-(1+i)^(-n) )
P = (200000*0.00445833333333333)/(1-(1+0.00445833333333333)^(-360))
P = 1116.82738940597
P = 1116.83
The monthly payment is $1,116.83
You can use a mortgage payment calculator to confirm this.
Here's one such calculator
https://www.bankrate.com/calculators/mortgages/amortization-calculator.aspx
I strongly recommend using a calculator like that because doing these calculations by hand are often tedious, and it makes sense to rely on a specialized calculator. Many if not all bankers use such calculators anyway.
However, it helps to use a formula so you can get a slight sense of what's going on rather than depend on a black box.
Also, this is a math class after all, so it makes sense to use a formula so you can show your work.
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To figure out how much of that monthly payment is interest, we will multiply the 0.00445833333333333 figure with the original loan balance L = 200,000
0.00445833333333333*L = 0.00445833333333333*(200,000) = 891.666666666667
This rounds to 891.67
So for the first month, you'll pay $891.67 in interest and ($1,116.83) - ($891.67) = $225.16 in principal. The remaining balance is the difference of the old previous balance minus the principal payment.
The figure 891.67 only applies for the first month. It will change for the other months because we'll apply that 0.00445833 figure to the remaining balance (not the 200,000) meaning that the interest payments will steadily go down.
Unfortunately, you'll be paying a significant chunk of the first monthly payment as interest.
In this case, roughly (891.67)/(1,116.83) = 0.798 = 79.8% of the first monthly payment is made in interest.
However, as mentioned in the paragraph earlier, the interest payment amount will go down which ultimately means the percentage goes down too. This decrease may be slow.
Side note: the calculator in the link I gave earlier has the option to show the amortization table or schedule. This is a very handy tool to keep track of your remaining balance, along with how much interest and principal was paid for any given month.
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Summary:
monthly payment = $1,116.83
first month's interest = $891.67
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