Find the maturity value of a loan of $2,900.00 after two years. The loan carries a simple interest rate of 7.7% per year The maturity value of a loan is $. (Round to the nearest cent as needed.) H-4

FINANCIAL ACCOUNTING
10th Edition
ISBN:9781259964947
Author:Libby
Publisher:Libby
Chapter1: Financial Statements And Business Decisions
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### Simple Interest Calculation

#### Problem Statement:
**Find the maturity value of a loan of $2,900.00 after two years. The loan carries a simple interest rate of 7.7% per year.**

---

#### Solution:
To find the maturity value of the loan, we need to calculate the interest earned over the given period and add it to the principal amount.

**Step-by-Step Solution:**

1. **Principal Amount (P):** $2,900.00
2. **Time Period (T):** 2 years
3. **Annual Interest Rate (R):** 7.7%

The formula to calculate simple interest is:
\[ \text{Interest} (I) = P \times R \times T \]

4. Convert the interest rate from a percentage to a decimal for calculation:
\[ R = 7.7\% = \frac{7.7}{100} = 0.077 \]

5. Substitute the values into the formula:
\[ I = 2900 \times 0.077 \times 2 \]

6. Perform the multiplication:
\[ I = 2900 \times 0.154 = 446.60 \]

7. The total interest earned is $446.60.

8. **Maturity Value (A):** This is the sum of the principal amount and the interest earned.
\[ A = P + I = 2900 + 446.60 = 3346.60 \]

---

**The maturity value of the loan is $3,346.60.**
(Round to the nearest cent as needed.)

![Image not provided in the explanation]
Transcribed Image Text:### Simple Interest Calculation #### Problem Statement: **Find the maturity value of a loan of $2,900.00 after two years. The loan carries a simple interest rate of 7.7% per year.** --- #### Solution: To find the maturity value of the loan, we need to calculate the interest earned over the given period and add it to the principal amount. **Step-by-Step Solution:** 1. **Principal Amount (P):** $2,900.00 2. **Time Period (T):** 2 years 3. **Annual Interest Rate (R):** 7.7% The formula to calculate simple interest is: \[ \text{Interest} (I) = P \times R \times T \] 4. Convert the interest rate from a percentage to a decimal for calculation: \[ R = 7.7\% = \frac{7.7}{100} = 0.077 \] 5. Substitute the values into the formula: \[ I = 2900 \times 0.077 \times 2 \] 6. Perform the multiplication: \[ I = 2900 \times 0.154 = 446.60 \] 7. The total interest earned is $446.60. 8. **Maturity Value (A):** This is the sum of the principal amount and the interest earned. \[ A = P + I = 2900 + 446.60 = 3346.60 \] --- **The maturity value of the loan is $3,346.60.** (Round to the nearest cent as needed.) ![Image not provided in the explanation]
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