Use the amortization table below to find the monthly mortgage payment for a $226,000 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'
Answer (2)
The monthly mortgage payment for a $226,000 loan at an interest rate of 6.50% for 30 years is calculated to be 1428.48. This is determined using the amortization table and involves finding the payment per $1000, calculating the number of thousands in the loan, and multiplying those values. After rounding, the final payment is 1428.48.
;
Find the monthly mortgage payment per $1000 from the table: $6.3207.
Calculate the number of thousands in the loan amount: 226 , 000/1000 = 226 .
Multiply the monthly mortgage payment per $1000 by the number of thousands in the loan amount: 226 × 6.3207 = 1428.4782 .
Round the result to the nearest cent: 1428.48 . The monthly mortgage payment is 1428.48 .
Explanation
Understanding the Problem We are given a loan of $226,000 at an interest rate of 6.50% for a term of 30 years. We are also provided with an amortization table that shows the monthly mortgage payment per $1000 of the loan. Our goal is to find the total monthly mortgage payment for this loan.
Finding Payment per $1000 First, we need to find the monthly mortgage payment per $1000 from the table for a 6.50% interest rate and a 30-year loan term. Looking at the table, we find that the monthly mortgage payment per $1000 is $6.3207.
Calculating Number of Thousands Next, 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 : 1000 226 , 000 = 226 $
So, there are 226 thousands of dollars in the loan.
Calculating Total Monthly Payment Now, we multiply the monthly mortgage payment per 1000 b y t h e n u mb ero f t h o u s an d s in t h e l o anam o u n tt 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 : 226 × 6.3207 = 1428.4782 $
Rounding to Nearest Cent Finally, we round the result to the nearest cent, which gives us $1428.48.
Final Answer Therefore, the monthly mortgage payment for a $226,000 loan at 6.50% for 30 years is $1428.48.
Examples
Understanding amortization is crucial in personal finance. For instance, when purchasing a car or a home, an amortization table helps you see how much of each payment goes towards the principal versus the interest. This knowledge enables you to make informed decisions about prepaying loans or understanding the total cost of borrowing over time. It's a fundamental tool for managing debt and planning your financial future effectively.
