You took a loan to buy a new car. After agreeing to pay $60,000 in interest in 410 days at 8.25% ordinary interest, how much was your loan?
Answer (2)
Define variables: P = principal, I = interest, r = interest rate, t = time in years.
Convert time to years: t = 360 410 .
Use the formula for ordinary interest: I = P ⋅ r ⋅ t .
Solve for P : P = r ⋅ t I = 0.0825 ⋅ 360 410 60000 ≈ 638580.93 .
Explanation
Understanding the Problem We are given that the interest paid on a loan is $60 , 000 , the time period is 410 days, and the ordinary interest rate is 8.25% . We need to find the principal loan amount.
Defining Variables and Given Values Let P be the principal loan amount, I be the interest paid, t be the time period in years, and r be the ordinary interest rate. We have:
I = $60 , 000 t = 410 days = 360 410 years (using the ordinary interest convention) r = 8.25% = 0.0825
Stating the Interest Formula The formula for ordinary interest is:
I = P ⋅ r ⋅ t
Substituting Values Substituting the given values into the formula, we get:
$60 , 000 = P ⋅ 0.0825 ⋅ 360 410
Solving for the Principal Now, we solve for P :
P = 0.0825 ⋅ 360 410 $60 , 000
P = 0.0825 ⋅ 360 410 $60 , 000 ≈ $638580.93
Final Answer Therefore, the principal loan amount is approximately $638 , 580.93 .
Examples
Understanding loans and interest calculations is crucial in personal finance. For example, when buying a house, you take out a mortgage, which is a type of loan. Knowing how the interest is calculated helps you determine the total cost of the house over the life of the loan and compare different loan offers. This understanding enables you to make informed decisions and manage your finances effectively.
The principal amount of the loan can be calculated using the ordinary interest formula, resulting in an approximate value of $631,169.89. This calculation considers the interest paid, interest rate, and time in years. Knowing this helps in understanding personal finance and loan management.
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