Compute the principal (in $) for the loan. Use ordinary interest when time is stated in days.
| Principal | Rate (%) | Time | Interest |
| --------- | -------- | ------------- | -------- |
| | | 1 1/2 years | $495 |
| | | | |
Enter an exact number
Answer (1)
Convert the time to days: T im e = 1.5 × 360 = 540 days.
Convert the rate to a decimal: R a t e = 0.11 .
Apply the ordinary interest formula: 495 = P r in c i p a l × 0.11 × 360 540 .
Solve for the principal: P r in c i p a l = 0.11 × 540 495 × 360 = 3000 . The principal is 3000 .
Explanation
Understanding the Problem We are given the interest, rate, and time for a loan, and we need to find the principal. The interest is ordinary, meaning we'll use a 360-day year for calculations.
Converting Time to Days First, let's convert the time to days. Since the time is 1 1/2 years, which is 1.5 years, and we are using ordinary interest (360 days in a year), the time in days is: T im e = 1.5 × 360 = 540 days
Converting Rate to Decimal Next, convert the rate to a decimal. The rate is 11%, so as a decimal, it is: R a t e = 11% = 0.11
Applying the Interest Formula Now, we use the ordinary interest formula: I n t eres t = P r in c i p a l × R a t e × 360 T im e We are given that the interest is 495 , so w e ha v e : 495 = P r in c i p a l × 0.11 × 360 540 $
Solving for Principal Solve for the principal: P r in c i p a l = 0.11 × 540 495 × 360 P r in c i p a l = 59.4 178200 = 3000
Final Answer Therefore, the principal for the loan is $3000.
Examples
Understanding loan principals is crucial in personal finance. For instance, if you're planning to start a small business and need a loan, knowing how the principal, interest rate, and loan term affect your payments helps you make informed decisions. Suppose you borrow money to buy equipment; the principal is the initial amount you borrow. The interest is what the lender charges for the loan. Calculating these factors ensures you understand the total cost of borrowing and can budget accordingly, preventing financial strain and promoting business success.
