Use the amortization table below to find the monthly mortgage payment for a $223,000 loan at 6.50% for 30 years.
| Rate (%) | 15 Years | 20 Years | 30 Years |
|---|---|---|---|
| 5.00 | 7.9079 | 6.5996 | 5.3682 |
| 5.25 | 8.0388 | 6.7384 | 5.5220 |
| 5.50 | 8.1708 | 6.8789 | 5.6779 |
| 5.75 | 8.3041 | 7.0208 | 5.8357 |
| 6.00 | 8.4386 | 7.1643 | 5.9955 |
| 6.25 | 8.5742 | 7.3093 | 6.1572 |
| 6.50 | 8.7111 | 7.4557 | 6.3207 |
| 6.75 | 8.8491 | 7.6036 | 6.4860 |
| 7.00 | 8.9883 | 7.7530 | 6.6530 |
| 7.25 | 9.1286 | 7.9038 | 6.8218 |
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.
Answer (2)
The monthly mortgage payment for a $223,000 loan at 6.50% for 30 years is $1409.52. This is computed by determining the payment per $1000 from the amortization table and multiplying by the number of thousands in the loan amount. The final amount is rounded to the nearest cent.
;
Divide the loan amount by 1000: 223 , 000/1000 = 223 .
Find the monthly mortgage payment per $1000 from the table: $6.3207.
Multiply the number of thousands by the payment per thousand: 223 × 6.3207 = 1409.5161 .
Round to the nearest cent: 1409.52 .
Explanation
Understanding the Problem We are given a loan of $223,000 at an interest rate of 6.50% for a term of 30 years. We need to find the monthly mortgage payment using the provided amortization table. The table gives the monthly mortgage payment per $1000 of the loan.
Calculating Number of Thousands First, we need to determine how many thousands of dollars are in the loan amount. To do this, we divide the total loan amount by 1000: 223 , 000/1000 = 223 So, the loan is equivalent to 223 thousands of dollars.
Finding Payment per Thousand Next, we look up the monthly mortgage payment per $1000 for a 6.50% interest rate and a 30-year term in the table. The table shows that the monthly payment is $6.3207 per $1000.
Calculating Total Monthly Payment Now, we multiply the number of thousands in the loan (223) by the monthly payment per $1000 ( 6.3207 ) t o f in d t h e t o t a l m o n t h l y m or t g a g e p a y m e n t : 223 × 6.3207 = 1409.5161 $
Rounding to Nearest Cent Finally, we round the result to the nearest cent, which is two decimal places: 1409.5161 ≈ 1409.52 Therefore, the monthly mortgage payment is $1409.52.
Final Answer The monthly mortgage payment for a $223,000 loan at 6.50% for 30 years is $1409.52.
Examples
Understanding amortization tables and calculating mortgage payments is crucial in personal finance. For example, when buying a house, you can use these tables to estimate your monthly payments based on the loan amount, interest rate, and loan term. This helps in budgeting and comparing different loan options to make informed financial decisions. Knowing how to calculate these payments ensures you understand the financial commitment involved in taking out a mortgage.
