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 | Maturity value |
| --------- | ------------- | ------------- | ----------- | ---------- | -------- | -------------- |
| $1,800 | 7% | March 09 | June 14 | | | |
Answer (1)
Calculate the exact time between March 09 and June 14, which is 97 days.
Calculate the interest using the formula I n t eres t = P r in c i p a l × R a t e × T im e /360 , resulting in I n t eres t = 1800 × 0.07 × ( 97/360 ) = $33.95 .
Calculate the maturity value using the formula M a t u r i t y Va l u e = P r in c i p a l + I n t eres t , resulting in M a t u r i t y Va l u e = 1800 + 33.95 = $1 , 833.95 .
The exact time is 97 days, the interest is $33.95 , and the maturity value is $1 , 833.95 .
Explanation
Understanding the Problem We are given a principal amount of $1 , 800 borrowed on March 09 at an interest rate of 7% and repaid on June 14. We need to find the exact time (in days), the interest, and the maturity value using ordinary interest.
Calculating Exact Time First, we need to calculate the number of days between March 09 and June 14. Using the Days in a year table or a calculator, we find that the number of days is 97.
Calculating Interest Next, we calculate the ordinary interest using the formula: I n t eres t = P r in c i p a l × R a t e × T im e /360 Substituting the given values, we have: I n t eres t = 1800 × 0.07 × ( 97/360 ) I n t eres t = 1800 × 0.07 × 0.26944 I n t eres t = 33.947 Rounding to the nearest cent, the interest is $33.95 .
Calculating Maturity Value Now, we calculate the maturity value using the formula: M a t u r i t y Va l u e = P r in c i p a l + I n t eres t Substituting the values, we have: M a t u r i t y Va l u e = 1800 + 33.95 M a t u r i t y Va l u e = 1833.95 The maturity value is $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 calculations 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. Knowing how to calculate interest helps you understand the true cost of borrowing and the potential earnings from savings. For example, if you deposit $1000 in a savings account with a 5% annual interest rate, you can calculate the interest earned in a year to be $1000 × 0.05 = $50 . This knowledge empowers you to make informed financial decisions.
