Answered

Use the amortization table below to find the monthly mortgage payment for a $253,000 loan at 6.25% for 20 years.




\multicolumn{4}{|c|}{Monthly Mortgage Payment per \$1000}

Rate (\%)		15 Years20 Years30 Years

5.00		7.90796.59965.3682

5.25		8.03886.73845.5220

5.50		8.17086.87895.6779

5.75		8.30417.02085.8357

6.00		8.43867.16435.9955

6.25		8.57427.30936.1572

6.50		8.71117.45576.3207

6.75		8.84917.60366.4860

7.00		8.98837.75306.6530

7.25		9.12867.90386.8218






State your answer in terms of dollars rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.

Verified Answer :

  • Identify the payment factor of \(7.3093\) from the table for a \(6.25\%\) interest rate and \(20\)-year term.
  • Determine the number of \(\$1,000\) units in the \(\$253,000\) loan, which is \(253\).
  • Multiply the units by the factor: \(253 \times 7.3093 = 1849.2529\).
  • Round the result to the nearest cent, which is \(\boxed{1849.25}\).

Explanation

  1. Identifying the Payment Factor

To determine the monthly mortgage payment, we first identify the relevant payment factor from the provided amortization table. For a loan with an interest rate of \(6.25\%\) and a term of \(20\) years, we look at the row corresponding to \(6.25\%\) and the column for \(20\) years. The table indicates that the payment factor per \(\$1,000\) is \(7.3093\).

  1. Calculating the Loan Units

The loan amount given is \(\$253,000\). Since the payment factor is based on increments of \(\$1,000\), we calculate the total number of thousands in the loan by dividing the total amount by \(1,000\):
\[N = \frac{253,000}{1,000} = 253\]
This means there are \(253\) units of \(\$1,000\) in the total loan amount.

  1. Calculating and Finalizing the Monthly Payment

Now, we calculate the total monthly payment \(P\) by multiplying the number of units by the payment factor \(F\):
\[P = N \times F = 253 \times 7.3093\]
Performing this calculation, we get:
\[P = 1,849.2529\]
Finally, rounding the result to the nearest cent, we arrive at the monthly mortgage payment of \(1,849.25\).

Examples

Understanding how to read an amortization table is a vital skill for anyone planning to take out a loan, such as a mortgage or a car loan. By knowing how to apply the payment factor, you can effectively compare different loan terms and interest rates to understand how they impact your monthly budget. This practice helps in making informed financial decisions, ensuring you are prepared for long-term commitments.

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