Concept explainers
Amortization gives the borrower an advantage: by paying more than the minimum required payment, the borrower can pay off (amortize) the principal faster and save money in interest. Assume P is the loan amount or principal, r is the interest rate, n is the compounding frequency, and t is the time in years. The amortization formula is used to determine the payment amount p that will amortize the loan in t years. However, if the borrower consistently pays Q, where
Business: Home Loan. The Begays finance $200,000 for a 30-yr home mortgage at an annual interest rate of 5%, compounded monthly.
a. Find the monthly payment needed to amortize this loan in 30 yr.
b. Assuming that the Begays make the payment found in part (a) every month for 30 yr, find the total interest they will pay.
c. Suppose the Begays pay an extra 15% every month (thus,
). Find the time needed to amortize the $200,000 loan.
d. About how much total interest will the Begays pay if they pay Q every month?
e. About how much will the Begays save on interest if they pay Q rather than p every month?
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Calculus and Its Applications (11th Edition)
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