Select the correct answer.
Walter took out a $6,000 loan for six years. He is being charged 6 percent interest, compounded annually. Calculate the total amount he will pay.
[tex]total amount = P(1+i)^t[/tex]
A. $7657.69
B. $8040.57
C. $8511.12
Answer (2)
Identify the principal (P), interest rate (i), and time (t).
Substitute these values into the compound interest formula: total amount = P ( 1 + i ) t .
Calculate ( 1 + i ) t = ( 1 + 0.06 ) 6 = 1.418519112256 .
Multiply by the principal: total amount = 6000 × 1.418519112256 = 8511.114673536 . The total amount is $8511.12 .
Explanation
Understanding the Problem We are given the principal amount of a loan, the interest rate, and the time period. We need to calculate the total amount to be paid using the formula for compound interest. The formula is: total amount = P ( 1 + i ) t , where P is the principal amount, i is the interest rate, and t is the time period.
Identifying Given Values We are given: Principal amount (P) = $6,000 Time period (t) = 6 years Interest rate (i) = 6% = 0.06
Substituting Values into the Formula Substitute the given values into the formula: total amount = 6000 ( 1 + 0.06 ) 6 total amount = 6000 ( 1.06 ) 6
Calculating the Power Calculate ( 1.06 ) 6 :
( 1.06 ) 6 = 1.418519112256
Calculating the Total Amount Multiply the result by 6000 :
total amount = 6000 × 1.418519112256 = 8511.114673536
Selecting the Correct Answer The total amount is approximately $8511.11. Comparing this with the given options, the correct answer is C. $8511.12
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 future savings. Similarly, when taking out a loan, understanding the total repayment amount, including compounded interest, allows you to budget effectively and avoid financial strain. This concept applies to various scenarios, from savings accounts to mortgages, making it a fundamental tool in personal finance.
To find the total amount Walter will pay on his $6,000 loan with 6% interest compounded annually over 6 years, we use the compound interest formula. The correct total amount is approximately $8,511.12, matching option C. This highlights the importance of understanding compound interest in financial decisions.
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