 On March 23, 2007, Mary Ann applied for a ₱48,000 loan at 9.5% simple interest. She 
promised to pay on July 12, 2007. Compute for the interest of the loan using: (a) 
Actual time, exact interest (b) Approximate time, exact interest (c) Actual time, 
ordinary interest (d) Approximate time, ordinary interest. PLEASE USE THE ORIGINAL FORMULA NO NEED FOR EXPLANATION JUST SHOW ME THE COMPURATIONS TO SOLUTUIONS

Certainly! Below are the computations for each case using the original formulas:

### Given:
- Principal (P) = ₱48,000
- Interest rate (r) = 9.5% per annum = 0.095
- Loan period: March 23, 2007 to July 12, 2007

### 1. Actual time, exact interest
- **Actual days** from March 23, 2007 to July 12, 2007: 111 days
- **Exact interest** (365 days per year):

\[
\text{Interest} = P \times r \times \frac{\text{Time in days}}{365} = 48{,}000 \times 0.095 \times \frac{111}{365} = ₱1{,}388.22
\]

### 2. Approximate time, exact interest
- **Approximate time**: 3 months + 19 days = 3 × 30 + 19 = 109 days
- **Exact interest** (365 days per year):

\[
\text{Interest} = P \times r \times \frac{\text{Time in days}}{365} = 48{,}000 \times 0.095 \times \frac{109}{365} = ₱1{,}363.56
\]

### 3. Actual time, ordinary interest
- **Actual days**: 111 days
- **Ordinary interest** (360 days per year):

\[
\text{Interest} = P \times r \times \frac{\text{Time in days}}{360} = 48{,}000 \times 0.095 \times \frac{111}{360} = ₱1{,}403.00
\]

### 4. Approximate time, ordinary interest
- **Approximate time**: 109 days
- **Ordinary interest** (360 days per year):

\[
\text{Interest} = P \times r \times \frac{\text{Time in days}}{360} = 48{,}000 \times 0.095 \times \frac{109}{360} = ₱1{,}377.33
\]

Let me know if you want further details or have any questions!

### Related Questions:
1. How do you calculate the number of days between two dates?
2. What is the difference between exact interest and ordinary interest?
3. Can you explain the difference between actual time and approximate time in simple interest calculations?
4. How does changing the number of days per year affect interest calculations?
5. What would happen if the loan period extended beyond a year?
6. How would compound interest calculations differ from simple interest in this scenario?
7. What are some real-life applications of these interest calculations?
8. How does the interest rate impact the total interest paid?

**Tip:** In finance, always verify whether the time base (360 or 365 days) is specified for interest calculations, as it significantly affects the results.

Learn how to compute simple interest for a loan based on different time periods and interest types. This problem involves calculating interest using exact and ordinary time methods. Suitable for high school students learning about financial mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation