Understanding Simple Interest
Simple interest is calculated using the formula:
Simple Interest = Principal × Rate × Time
The total amount after a certain period can be expressed as:
Amount = Principal + Simple Interest
In this scenario, we know the amount for 2 years and 3 years.
Given Information
- Amount after 2 years = 6200
- Amount after 3 years = 6200 + Simple Interest for 1 additional year
Calculating Simple Interest for 1 Year
Let the principal be P and the rate of interest be R%.
- Amount after 2 years:
A(2) = P + (P * R * 2) = 6200
- Amount after 3 years:
A(3) = P + (P * R * 3) = 6200 + (P * R)
From the second equation, we can derive:
A(3) = A(2) + (P * R)
This simplifies to:
6200 + (P * R) = 6200 + (P * R * 2) + (P * R)
Hence,
P * R = 6200 - 6200 = 0
This indicates that the interest for the 1-year period must also yield the same amount, allowing us to establish a relationship.
Calculating Principal and Rate
- Assuming P = 6200 - (P * R * 2)
From the first equation, we can derive the rate:
P * R = (6200 - P) / 2
This leads to two equations that can be solved simultaneously to find the values for P and R.
Final Values
After solving, we find:
- Principal (P) = 5000
- Rate of Interest (R) = 12%
This provides a clear understanding of how simple interest works with the given amounts.