Simple Interest
Simple interest is calculated on the principal sum only. The formula for simple interest is:
$$ I = P \cdot r \cdot t $$
where:
- \( I \) is the interest,
- \( P \) is the principal sum,
- \( r \) is the interest rate,
- \( t \) is the time period.
Compound Interest
Compound interest takes into account the interest that accumulates on both the initial principal and the interest that has previously been added. The formula for compound interest is:
$$ I = P \cdot (1 + r)^n - 1 $$
where:
- \( I \) is the interest,
- \( P \) is the principal sum,
- \( r \) is the interest rate,
- \( n \) is the number of periods.
Simple Interest Calculation Example
If you borrow £100 for 1 year at a 15% interest rate, the interest would be:
$$ I = 100 \cdot 0.15 \cdot 1 = £15 $$
Compound Interest Calculation Example
If £500 is loaned for two years at an interest rate of 12% per annum, compounded quarterly, the calculations are as follows:
- Number of periods \( n = 4 \cdot 2 = 8 \)
- Quarterly interest rate \( r = \frac{12}{4} = 3% = 0.03 \)
The interest \( I \) would be:
$$ I = 500 \cdot (1.03)^8 - 1 = £133.38 $$
Importance
Interest rates play a crucial role in the economy:
- Influences Consumer Spending: Higher interest rates can dampen spending and borrowing.
- Impacts Investment: Companies may delay or hasten investment based on interest rate trends.
- Guides Monetary Policy: Central banks use interest rates to control inflation and stabilize the economy.
- Usury: Charging excessively high interest rates.
- APR (Annual Percentage Rate): The annual rate charged for borrowing, encompassing interest and fees.
- Yield: The earnings generated and realized on an investment over a specific period.
FAQs
What is the difference between interest rate and APR?
The interest rate is the cost of borrowing the principal, while APR includes additional fees or costs associated with the transaction.
How does compound interest benefit investors?
Compound interest generates interest on both the initial principal and the accumulated interest from previous periods, leading to exponential growth.