Find the maturity value FV of the given loan amount. (Round your answer to the nearest cent.)
$2,252 borrowed at 12.125% from March 10 through December 20 of the same year

To calculate the maturity value $ FV $ of the loan, we can use the **simple interest formula**:

\[
FV = P(1 + rt)
\]

Where:
- $ P $ is the principal (loan amount),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time in years.

### Step 1: Assign values to the variables
- Principal, $ P = 2252 $
- Interest rate, $ r = 12.125\% = 0.12125 $
- Time, $ t $ is the fraction of the year from March 10 to December 20.

### Step 2: Calculate the time period $ t $
We need to find the number of days between March 10 and December 20. 

- From March 10 to December 20:  
  March 10 - March 31 = 21 days (March has 31 days)  
  April = 30 days  
  May = 31 days  
  June = 30 days  
  July = 31 days  
  August = 31 days  
  September = 30 days  
  October = 31 days  
  November = 30 days  
  December 1 - December 20 = 20 days  

Total days = 21 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 20 = **285 days**.

Since a year has 365 days, the time $ t $ is:

\[
t = \frac{285}{365}
\]

### Step 3: Plug values into the formula

\[
FV = 2252 \left(1 + 0.12125 \times \frac{285}{365}\right)
\]

Let me calculate this for you.The maturity value $ FV $ of the loan is approximately **$2,465.21** when rounded to the nearest cent.

Would you like further details or explanations?

Here are 5 related questions to explore:
1. How would the maturity value change if the interest rate were higher?
2. How does simple interest differ from compound interest in long-term loans?
3. What would the maturity value be if the loan term was extended to a full year?
4. How would the calculation differ if the loan was paid back in installments?
5. What are the advantages of paying off a loan early?

**Tip:** Always double-check the time period when calculating interest, especially if leap years are involved!

Find the maturity value FV of the given loan amount. (Round your answer to the nearest cent.) $2,252 borrowed at 12.125% from March 10 through December 20 of the same year.

Learn how to calculate the maturity value of a $2,252 loan at 12.125% simple interest, from March 10 through December 20. Follow the step-by-step solution using the simple interest formula and time calculation. Suitable for high school students studying loan interest calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation