Select the correct answer.
Alisha has a $[tex]15,000[/tex] car loan with a 6 percent interest rate that is compounded annually. How much will she have paid at the end of the five-year loan term?
total amount $[tex]=P(1+i)^t[/tex]
A. $[tex]19,500.25[/tex]
B. $[tex]15,900.50[/tex]
C. $[tex]20,073.50[/tex]
Answer (1)
Identify the principal amount (P), interest rate (i), and time period (t).
Substitute the values into the formula: total amount = P ( 1 + i ) t .
Calculate the total amount: total amount = 15000 × ( 1 + 0.06 ) 5 = 20073.383664 .
Select the correct answer: $20 , 073.50
Explanation
Identify Given Values First, we need to identify the given values from the problem. Alisha has a car loan of $15 , 000 , which is the principal amount (P). The interest rate is 6 percent, or 0.06 as a decimal (i). The loan term is 5 years (t). The formula for the total amount is given as: total amount = P ( 1 + i ) t
Substitute Values into Formula Now, we substitute the values into the formula: total amount = 15000 × ( 1 + 0.06 ) 5
Calculate Total Amount Next, we calculate the total amount. total amount = 15000 × ( 1.06 ) 5 . total amount = 15000 × 1.3382255776 . total amount = 20073.383664
Select Correct Answer Finally, we compare the calculated total amount with the given options. The calculated total amount is approximately $20 , 073.38 , which is closest to option C. Therefore, the correct answer is C.
Examples
Understanding compound interest is crucial for making informed financial decisions. For instance, when planning for retirement, knowing how your investments grow over time with compound interest helps you estimate your potential savings. Similarly, when taking out a loan, understanding the total repayment amount, including interest, allows you to budget effectively and avoid financial strain. This concept applies to various scenarios, such as mortgages, savings accounts, and credit card debt, making it an essential tool for financial literacy.
