Calculate the simple interest and maturity value.
Note: Do not round intermediate calculations. Round your answers to the nearest cent.
| Principal | Interest rate | Time |
|---|---|---|
| $17,000 | 9 1/4 % | 18 months |
Answer (2)
Calculate the simple interest: Simple Interest = Principal × Interest Rate × Time = 17000 × 0.0925 × 1.5 = 2358.75 .
Calculate the maturity value: Maturity Value = Principal + Simple Interest = 17000 + 2358.75 = 19358.75 .
The simple interest is $2358.75 .
The maturity value is $19358.75 .
Explanation
Understanding the Problem We are given the principal amount, the interest rate, and the time period. We need to calculate the simple interest and the maturity value.
Identifying Given Values First, let's identify the given values:
Principal (P) = $17,000 Interest rate (R) = $9\frac{1}{4}% = 9.25% = 0.0925 Time (T) = 18 months = 1.5 years
Calculating Simple Interest Now, we calculate the simple interest using the formula:
Simple Interest (SI) = P * R * T SI = $17,000 * 0.0925 * 1.5 SI = $2358.75
Calculating Maturity Value Next, we calculate the maturity value using the formula:
Maturity Value (MV) = Principal + Simple Interest MV = $17,000 + $2358.75 MV = $19358.75
Final Answer Therefore, the simple interest is $2358.75 and the maturity value is $19358.75.
Examples
Understanding simple interest and maturity value is crucial in personal finance. For example, if you deposit $17 , 000 into a savings account with an annual interest rate of 9.25% for 1.5 years, you can calculate the interest earned and the total value of your investment at the end of the period. This concept is also applicable when calculating interest on loans or bonds, helping you understand the cost of borrowing or the return on investment. Knowing these calculations allows you to make informed financial decisions, whether you're saving, investing, or borrowing money. The simple interest earned is $2358.75 , and the maturity value is $19358.75 .
The simple interest calculated is $2,368.75, and the maturity value is $19,368.75. This is done using the principal amount, interest rate, and time to find both values. These calculations help in understanding the total interest earned and the final amount after an investment period.
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