Maximum Affordable Mortgage Calculation

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In summary, Alice wants to take out a 20-year mortgage with an 8% interest rate compounded semi-annually. She can afford monthly payments of $850. Using a graphing calculator, the largest mortgage she can afford is $119,628.45. However, without using a calculator, after correcting a mistake in the calculation, the largest mortgage she can afford is $102,612.70.
  • #1
physicsgal
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Homework Statement


alice wants to take out a 20 yr mortage. the interest rate is 8% compounded semi-annually. alice can afford monthly payments of $850. what is the largest mortage that she can afford?


Homework Equations





The Attempt at a Solution


this is using a graphing calculator:
N= 20 x 12 = 240
I%= 8
*PV= 102 612.70?
PMT= -850
FV = 0
P/Y = 12
C/Y = 2
PMT = END

but I am suppose to solve this without a graphing calculator.

PV = (R(1-(1/1+i)^n)/i

R = 850
n = 240
i = ?
for i i had 1.04^(1/8) - 1 = 0.004914626.. i think that's where my problem is. but dunno.

for the answer i got $119,628.45... but that doesn't match the $102,612.70 from my graphing calculator.

any help is appreciated

~Amy
 
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  • #2
physicsgal said:

Homework Statement


alice wants to take out a 20 yr mortage. the interest rate is 8% compounded semi-annually. alice can afford monthly payments of $850. what is the largest mortage that she can afford?


Homework Equations





The Attempt at a Solution


this is using a graphing calculator:
N= 20 x 12 = 240
This, immediately, is wrong. N is the number of "compounding intervals". If this is "compounded semi-annually" for 20 years, how many times is it compounded?

I%= 8
*PV= 102 612.70?
PMT= -850
FV = 0
P/Y = 12
C/Y = 2
PMT = END

but I am suppose to solve this without a graphing calculator.

PV = (R(1-(1/1+i)^n)/i

R = 850
n = 240
i = ?
8% of course: 0.08 so 1+ i= 1.08.

for i i had 1.04^(1/8) - 1 = 0.004914626.. i think that's where my problem is. but dunno.

for the answer i got $119,628.45... but that doesn't match the $102,612.70 from my graphing calculator.

any help is appreciated

~Amy
 
  • #3
Now since its compounded 2 times a year for 20 years its compounded 40 times.
Since we've fixed your expression for total she can pay, which is 204,000, set them equal and solve for the original value.
 
  • #4
thanks for the help. but it turns out that instead of 1.04^(1/8) - 1 = 0.004914626.. it should have been 1.04^(1/6) -1 =0.006558197.. that gives me $102,612.70 (same answer as i got with the graphing calculator).

~Amy
 

1. How do I calculate my monthly mortgage payment?

To calculate your monthly mortgage payment, you will need to know the principal amount of your loan, the interest rate, and the length of your loan in years. To simplify the calculation, you can use the following formula: monthly payment = (principal * [interest rate / 12]) / (1 - (1 + [interest rate / 12])^(-n)), where n is the total number of monthly payments.

2. What is the difference between a fixed-rate and adjustable-rate mortgage?

A fixed-rate mortgage means that the interest rate will remain the same for the entire term of the loan. This allows for predictable monthly payments. An adjustable-rate mortgage (ARM) has an interest rate that can change over time, typically after an initial fixed-rate period. This means that your monthly payments may increase or decrease depending on market conditions.

3. How does my credit score affect my mortgage rate?

Your credit score is a major factor in determining your mortgage rate. A higher credit score typically results in a lower interest rate, as it reflects a lower risk for the lender. It is important to maintain a good credit score to secure a favorable mortgage rate.

4. What is a down payment and how does it impact my mortgage?

A down payment is the initial payment made towards the purchase of a home. It is typically a percentage of the total cost of the home. The size of your down payment can impact your mortgage in several ways, including the interest rate, monthly payment, and the need for private mortgage insurance.

5. What is an amortization schedule?

An amortization schedule is a table that shows the breakdown of each mortgage payment, including the amount that goes towards the principal and interest. It also shows the remaining balance of the loan after each payment. This schedule can be helpful in understanding how your mortgage payments are distributed and how much interest you will pay over the life of the loan.

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