Final answer:Final answer:
To find the periodic payments PMT on a $20,000 loan at an 8% annual interest rate with monthly payments over 10 years, one would use the annuity formula, taking into account the present value, monthly interest rate, and total number of payments.
Step-by-step explanation:
To determine the periodic payments PMT on a loan, we need to use the loan's principal amount, interest rate, and the number of payment periods. In this case, we have a $20,000 loan at an 8% annual interest rate, with monthly payments over 10 years.
First, we need to recognize this is an application of the annuity formula, which is:
\[PMT = \frac{PV \cdot i}{1 - (1+i)^{-n}}\]
Where:
- PV = Present Value of the loan, which is $20,000
- i = Monthly interest rate (annual rate / 12), which is 0.08/12
- n = Total number of payments (years * 12), which is 10*12
Plugging in the values:
\[PMT = \frac{20000 \cdot \frac{0.08}{12}}{1 - (1+\frac{0.08}{12})^{-10\times12}}\]
After calculating the above expression (and rounding to the nearest cent), we will obtain the monthly payment amount.
A car loan or mortgage loan are good examples of a periodic payment note. The terms of the note call for the borrower to make periodic payments, usually monthly, until the loan amount has been paid in full.