Calculate the mortagage he could assume for each amortization period

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In summary, Bob can afford a monthly mortgage payment of $575 and with a current interest rate of 6.75%, he could assume a mortgage of $64,978.40 for a 15 year amortization period. The formula used for this calculation is P=(a(z^n-1))/(z^n(z-1)), where z=(1+i), a is the monthly payment, n is the number of payments, and i is the interest per payment. This can also be calculated using the formula A=Ao(1+i)^n, where A is the amount after, Ao is the amount before (principal amount), i is the interest rate, and n is the time period.
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Bob estimates he can afford a monthly mortgage payment of $575. Current interest rates are 6.75%. Calculate the mortagage hecould assume for each amortization period.
A) 15 years

the extra info is that the monthly payments per $1000 for this percentage + 15years is $8.85.

How would you do this problem? :confused:
 
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  • #2
Do you want to cheat
 
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What have you done so far?
 
  • #4
Actually most people who do this possesses a financial calculator. The formula is derived at http://www.moneychimp.com/articles/finworks/fmmortgage.htm

P(z^n)-a((z^n)-1)/(z-1) = debt remaining.

Here, z=(1+i), where i is interest per payment. a is the payment, P is the principal borrowed, and n is the number of payments made.
 
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  • #5
the formula used is A=Ao (1+ i) ^n
A= amount after
Ao=amount before ( principle amount)
i=interest rate
n=time period
 
  • #6
How about trying 575/8.5*1000=64972. Otherwise, amount assumed equals present value of future payments where interest interest is compounded monthly.
Mortgage Amount= 575* Sum[((1+(.0675/12))^(-k)),k=1,2,...,12*15]=
575* [1-(1+(.0675/12))^(-15*12)]/(.0675/12).
 
  • #7
answerseeker: the formula used is A=Ao (1+ i) ^n. That is not correct because we regularly subtract the monthly payment from the principal.

LittleWolf: How about trying 575/8.5*1000=64972. Sounds pretty good. Sum[((1+(.0675/12))^(-k)), As far as that goes, I don't think it does any good to sum.

My calculator, HP15C, takes it straight across from the formula I put previously. That is for this case:

[tex]P=\frac{a(z^n-1)}{z^n(z-1)}[/tex]

Putting in $575 for a, 1.005625 for z, n = 180, since it is a monthly payment. Then, I arrive at $64978.40. REMEMBER: 6% is not 6, it is .06 in decimal form. Thus 6.75%/12 = .005625.
 
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Related to Calculate the mortagage he could assume for each amortization period

What is a mortgage?

A mortgage is a type of loan that is used to purchase a property, typically a house or a piece of land. The borrower agrees to make regular payments to the lender over a set period of time, usually 15 or 30 years, until the loan is fully paid off.

What is an amortization period?

An amortization period is the length of time it takes to pay off a mortgage in full. During this time, the borrower will make regular payments that include both principal and interest, gradually reducing the amount owed until the loan is paid off.

How is the mortgage amount calculated?

The mortgage amount is calculated based on the price of the property, the interest rate, and the length of the amortization period. A mortgage calculator can be used to determine the monthly payments based on these factors.

What is the purpose of assuming a mortgage?

Assuming a mortgage means that a new borrower takes over the existing mortgage from the original borrower. This can be beneficial for the new borrower if the terms of the mortgage are favorable, such as a low interest rate. It can also save the new borrower from having to go through the process of obtaining a new mortgage.

How can the mortgage amount be adjusted for different amortization periods?

The mortgage amount can be adjusted by changing the length of the amortization period. A longer amortization period will result in lower monthly payments, but a higher amount of interest paid over the life of the loan. A shorter amortization period will result in higher monthly payments, but a lower amount of interest paid overall.

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