Complete the following, using ordinary interest. (Use Days in a year table.) Note: Do not round intermediate calculations. Round the "Interest" and "Maturity value" to the nearest cent.
| Principal | Interest rate | Date borrowed | Date repaid | Exact time | Interest |
|---|---|---|---|---|---|
| $1,800 | 7 % | March 09 | June 14 | | |
Answer (2)
Calculate the exact time (number of days) between March 09 and June 14: 97 days.
Calculate the ordinary interest: Interest = Principal * Rate * Time / 360 = $1,800 * 0.07 * (97 / 360) = $33.95.
Calculate the maturity value: Maturity Value = Principal + Interest = $1,800 + $33.95 = $1,833.95.
The interest is $33.95 and the maturity value is $1 , 833.95 .
Explanation
Understanding the Problem We are given a principal of $1,800, an interest rate of 7%, a date borrowed of March 09, and a date repaid of June 14. We need to find the exact time (number of days) between March 09 and June 14, the interest, and the maturity value using ordinary interest.
Calculating the Exact Time First, we need to find the number of days between March 09 and June 14. We can use the Days in a year table to find the corresponding day of the year for each date. March 09 is the 68th day of the year. June 14 is the 165th day of the year. So, the exact time (number of days) is 165 - 68 = 97 days.
Calculating the Interest Next, we calculate the ordinary interest using the formula: Interest = Principal * Rate * Time / 360 Interest = $1,800 * 0.07 * (97 / 360) Interest = $33.95
Calculating the Maturity Value Then, we calculate the maturity value using the formula: Maturity Value = Principal + Interest Maturity Value = $1,800 + $33.95 Maturity Value = $1,833.95
Final Answer Therefore, the exact time is 97 days, the interest is $33.95, and the maturity value is $1,833.95.
Examples
Understanding simple interest is crucial in everyday financial transactions. For instance, when you deposit money in a savings account, the bank pays you interest. Similarly, when you borrow money, you pay interest to the lender. Calculating the exact interest and maturity value helps you understand the true cost or benefit of these transactions. Knowing these calculations allows you to make informed decisions about savings, loans, and investments, ensuring you're not caught off guard by hidden costs or missed opportunities. For example, if you borrow $1000 at a 5% interest rate for 2 years, you can calculate the total interest you'll pay and the total amount you'll need to repay.
The exact time between March 09 and June 14 is 97 days. The interest calculated is $33.95, and the maturity value is $1,833.95. These calculations help understand the cost associated with borrowing money using ordinary interest.
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