Simple Interest and Its Comparisons

Questions and Answers

What is the correct formula for calculating Simple Interest (SI)?

SI = P + R × T

SI = P(1 + R) × T

SI = P × (R + T)

SI = P × R × T (correct)

Which of the following statements is true regarding Simple Interest compared to Compound Interest?

Simple Interest results in a constant interest amount over time. (correct)

Compound Interest results in less total interest paid compared to Simple Interest.

Simple Interest results in exponential growth over time.

Simple Interest is calculated on the principal and accumulated interest.

If $1,000 is invested at a rate of 5% simple interest for 3 years, what is the total amount at the end of the investment period?

$1,300

$1,150 (correct)

$1,200

$1,050

Which of these scenarios typically use Simple Interest calculations?

Personal loans from banks Signup and view all the answers

Which formula represents how to find the Total Amount (A) with Simple Interest?

A = P + (P × R × T) Signup and view all the answers

In Simple Interest calculation, which variable represents the interest rate per period?

R Signup and view all the answers

Why is Simple Interest preferred for short-term loans?

It results in less overall interest paid. Signup and view all the answers

Which of the following examples is least likely to use Simple Interest?

Credit card payments Signup and view all the answers

Study Notes

Simple Interest

Formula Derivation

Basic Formula: Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)
Units:
- P: Principal amount (initial investment)
- R: Rate of interest per period (in decimal form; e.g., 5% = 0.05)
- T: Time (number of periods; e.g., years)
Derived Formula:
- To find Total Amount (A): A = P + SI
- A = P + (P × R × T) = P(1 + RT)

Comparison With Compound Interest

Simple Interest:
- Interest calculated only on the principal.
- Formula: SI = P × R × T.
- Typically results in less total interest paid over time compared to compound interest.
Compound Interest:
- Interest calculated on the principal and also on accumulated interest.
- Formula: CI = P (1 + R/n)^(nT) - P (where n is the number of compounding periods per year)
- Results in exponential growth of the investment over time due to "interest on interest."

Calculating Interest Over Time

Example Calculation:
- Given P = $1,000, R = 5% (0.05), T = 3 years.
- SI = 1000 × 0.05 × 3 = $150.
- Total Amount = P + SI = 1,000+1,000 + 1,000+150 = $1,150.
Key Points:
- Interest remains constant over time.
- Useful for short-term loans and investments.

Real-life Examples Of Simple Interest

Personal Loans: Banks often use simple interest for personal loans for a fixed duration.
Car Loans: Some car financing options may utilize simple interest.
Savings Accounts: Certain savings accounts might offer simple interest calculations.
Education Loans: Some educational loans charge simple interest during the study period.

Description

This quiz covers the fundamentals of simple interest, including its formula derivation and comparison with compound interest. Learn to calculate the total amount based on the principal, rate, and time, and understand the key differences between simple and compound interest. Perfect for students studying finance or mathematics concepts.