Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Decreasing the number of years of a loan decreases the amount of interest repaid over the term of the loan. Suppose a dental hygienist has the option of a 30-year loan or a 25-year loan of $345,000 at an annual interest rate of 3.75%.
(a)
a) Calculate the monthly payment (in dollars) for each loan. (Round your answers to the nearest cent.)
30-year loan
25-year loan

b) Calculate the savings in interest (in dollars) by using the 25-year loan. (Round your answer to the nearest cent.)

Sagot :

sqdancefan

Answer:

  a) 30 yr: $1597.75; 25 yr: $1773.75

  b) $43065.00

Step-by-step explanation:

The monthly payment for each loan can be found using the amortization formula, or a spreadsheet or calculator. The shorter 25-year loan has fewer and larger payments, but the net result is less interest paid.

a)

The attached calculator shows the monthly payments to be ...

  30 year loan: $1597.75 monthly

  25 year loan: $1773.75 monthly

b)

The number of payments is the product of 12 payments per year and the number of years. The total repaid is the monthly payment times the number of payments.

The difference in amounts repaid is the difference in interest charged.

  360×1597.75 -300×1773.75 = $43065 . . . . savings using 25-year loan

__

Additional comment

The monthly payment on a loan of principal P at annual rate r for t years is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

Some calculators and all spreadsheets have built-in functions for calculating this amount.

View image sqdancefan
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.