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The Smiths took out a \(130,000, 30-year mortgage at an APR of 6.5%. The monthly payment was \)821.69. What will be their total interest charges after 30 years?

Short Answer

Expert verified
The total interest charges after 30 years will be $165,808.4

Step by step solution

01

Calculate Total Repayment Amount

First, determine the total repayment amount by multiplying the monthly repayment amount by the total number of repayments. In this case, multiply $821.69 by the total number of payments over 30 years, which is 30*12: \(821.69 \times 30 \times 12 = \$295,808.4\)
02

Calculate Total Interest charges

Next, determine the total interest charges by subtracting the original principal from the total repayment amount. In this case, subtract $130,000 from $295,808.4: \$295,808.4 - \$130,000 = \$165,808.4

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Total Repayment Amount
Understanding the total repayment amount on a mortgage is crucial for anyone planning to buy a home. This amount represents the sum of all payments made toward the mortgage over its lifetime, including interest and principal. To calculate this figure, you multiply the monthly payment by the number of payments you'll make over the term of the mortgage.

For the Smiths, who have a 30-year mortgage, you would calculate it as follows: the monthly payment of \(821.69 times 360 (30 years times 12 months per year) to get a total repayment amount of \)295,808.4. This total payment goes beyond just repaying the borrowed amount; it also includes the interest, which can sometimes exceed the original loan amount for longer mortgage terms or higher interest rates.
Amortization Schedule
An amortization schedule is an essential tool for homeowners because it breaks down each payment throughout the life of the mortgage and shows how much of each payment goes toward interest versus principal. Initially, a larger portion of each payment is allotted to interest, with the balance gradually shifting over time.

By creating an amortization schedule, borrowers can see exactly when their equity in the property increases and by how much after each payment. An amortization schedule can also inform you about how extra payments will affect your loan's lifespan and interest savings. For instance, if the Smiths were to make additional payments, the schedule would show them how much quicker they could pay off their loan and reduce the total interest charges.
Annual Percentage Rate (APR)
The annual percentage rate, or APR, is a broader measure of the cost to borrow money than the interest rate alone. The APR includes the interest rate as well as other charges or fees involved in securing the loan, spread over the term of the loan. This provides a more comprehensive view of the costs associated with the mortgage.

For example, a 6.5% APR indicates that the Smiths are paying an annual rate of 6.5% on their borrowed funds, which encompasses both the interest and any additional fees. It's important for them to compare the APR when shopping for mortgages as it affects the total repayment amount and monthly payments. A lower APR signifies fewer costs over the term of the loan and typically signals a better deal for the borrower.

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Most popular questions from this chapter

Allison has a mortgage with North End Bank. The bank requires that she pay her homeowner’s insurance, property taxes, and mortgage in one monthly payment. Her monthly mortgage payment is \(1,390, her semi-annual property tax bill is \)3,222, and her quarterly homeowner’s bill is $282. How much does Allison pay North End Bank each month?

The Ungers have an adjusted gross income of \(117,445. They are looking at a new house that would carry a monthly mortgage payment of \)1,877. Their annual property taxes would be \(6,780, and their semi-annual homeowner’s premium would be \)710. a. Find their front-end ratio to the nearest percent. b. Assume that their credit rating is good. Based on the front-end ratio, would the bank offer them a loan? Explain. c. The Ungers have a monthly car loan of \(430, and their aver- age monthly credit card bill is \)5,100. Mr. Unger is also paying $1,000 per month in child support from a previous marriage. Compute the back-end ratio to the nearest percent. d. If the bank used both the front-end and back-end ratios to decide on mortgage approval, would the Ungers get their mortgage? Explain.

Joe wants to rent an apartment with an initial monthly rent of \(\$ 1,400 .\) He has been told that the landlord raises the rent 1.25\(\%\) each year. Set up an exponential function that models this situation. Calculate the rent after 12 years. Round to the nearest dollar.

The square footage and monthly rental of 10 similar one-bedroom apartments yield the linear regression \(y=0.775 x+950.25,\) where \(x\) represents the square footage of the apartment and \(y\) represents the monthly rental price. Grace can afford \(\$ 1,500\) per month rent. Using the equation, what size apartment should she expect to be able to rent for that price?

United Bank offers a 15-year mortgage at an APR of 6.2%. Capitol Bank offers a 25-year mortgage at an APR of 6.5%. Marcy wants to borrow $120,000. a. What would the monthly payment be from United Bank? b. What would the total interest be from United Bank? Round to the nearest ten dollars. c. What would the monthly payment be from Capitol Bank? d. What would the total interest be from Capitol Bank? Round to the nearest ten dollars. e. Which bank has the lower total interest, and by how much? f. What is the difference in the monthly payments? g. How many years of payments do you avoid if you decide to take out the shorter mortgage?

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