# Calculate the mortagage he could assume for each amortization period

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.
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? Do you want to cheat What have you done so far? 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. Last edited: the formula used is A=Ao (1+ i) ^n A= amount after Ao=amount before ( principle amount) i=interest rate n=time period 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). 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: $$P=\frac{a(z^n-1)}{z^n(z-1)}$$ 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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## 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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