# Maths Problem Help: Balance Due on 30-Year Mortgage After 8 Years

• IB
In summary, the conversation discusses a mortgage obtained on a $275,000 home at 7.25% interest rate for 30 years, with a monthly payment of$1,875.99. After 8 years of payments, the conversation asks for the balance due on the mortgage, which can be calculated using a formula involving exponential functions or with the use of financial functions on a calculator.
IB

a 30 year mortgage is obtained on a $275,000 home at a rate of 7.25%. The monthly payment is$1,875.99. After making payments for 8 years, what is the balance due on the mortgage?

IB said:

a 30 year mortgage is obtained on a $275,000 home at a rate of 7.25%. The monthly payment is$1,875.99. After making payments for 8 years, what is the balance due on the mortgage?

Let B(n) = balance after n payments
I(n) = monthly interest payment
A = amount of payment = $1,875.99 i = montly interest rate = 7.25%/12 I(n) = B(n-1)i B(0) =$275,000
B(1) = B(0) - (A - I(1)) = B(0) - (A - B(0)i)
B(2) = B(1) - (A - I(2)) = B(1) - (A - B(1)i)
B(3) = B(2) - (A - I(3)) = B(2) - (A - B(2)i)

etc

Problems like this can easily be done on a spreadsheet. You can also start expanding out the terms and see a progression. If you are learning how to do sums of series, then maybe that is what you are supposed to be doing here. The resulting formula involves a ratio involving exponential functions. The notation is a bit different, but you can find the result and other mortgage related equations here

http://www.econ.umn.edu/~cswan/econ5623/MortMath/MortMath.html

Last edited by a moderator:
Can you do it on a TI-calculator?

IB said:
Can you do it on a TI-calculator?

There are financial functions built into the TI-83 Plus, and probably the TI-83, and probably other calculators as well. You could also program many calculators to do this calculation. Get out your manual, or go to the TI website to download a manual. The financial function on the TI=83 Plus are under APPS. There is a data entry area for entering the parameters given in the problem, and a number of functions including one for balance. Be careful when you enter the data that you specify the data consistently. There are some functions that do not need all the data specified, and some that do not work unless you have the right set of data specified.

For example if you give it N=360, I=7.5%, PV=275000, and P/Y = 12, it will correctly calculate the payment as -1875.98477, but if you ask it for the balance after some number of payments and you have not filled in the correct payment, it will give you the wrong answer assuming the payment is whatever you put into (or was left in) the data bank. It works, but you have to be careful. It does not check for inconsistent data.

## 1. What is a 30-year mortgage?

A 30-year mortgage is a type of home loan that is paid off over a period of 30 years. It is a common choice for homeowners because it allows for a lower monthly payment compared to shorter loan terms.

## 2. How is the balance due on a 30-year mortgage calculated?

The balance due on a 30-year mortgage is calculated by subtracting the total amount of principal and interest payments made over the first 8 years from the original loan amount. This will give you the remaining balance on the mortgage.

## 3. What is the significance of the balance due after 8 years?

The balance due after 8 years is important because it gives an idea of how much of the mortgage has been paid off in the first 8 years. It can also be used to calculate the remaining payments needed to fully pay off the mortgage.

## 4. How does the interest rate affect the balance due on a 30-year mortgage?

The interest rate plays a significant role in the balance due on a 30-year mortgage. A higher interest rate will result in a larger balance due, as more interest is accumulated over the 8-year period. On the other hand, a lower interest rate will result in a smaller balance due.

## 5. Can I pay off the balance due on a 30-year mortgage before the 8 years are up?

Yes, you can pay off the balance due on a 30-year mortgage before the 8 years are up. However, depending on the terms of your mortgage, you may be subject to prepayment penalties. It is important to consult with your lender before making any extra payments towards your mortgage.

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