Simple and Compound Interest Explained

• The lecture will cover Simple and Compound Interest and how the knowledge from Percentages will be useful.

Overview

• Simple and Compound Interest are compared, including concepts, formulas, and tricks.
• The session includes concepts, numericals, and tricks for both Simple and Compound Interest.
• Practice problems will be included in the session.
• The goal is to establish a strong foundation to tackle any level of Simple and Compound Interest problems.

Difference Between Simple and Compound Interest

• It's explained with an example where ₹1000 is invested in both Simple and Compound Interest, both at a 10% rate of interest.
• Principal (P): The amount invested or borrowed.
• Interest (I): The additional amount the person receives above their investment.
• Amount (A): Principal + Interest.
• In Simple Interest, the rate of interest is applied to the original principal every year.
• In Compound Interest, the first year's interest is applied to the original principal, but subsequent years' interest is applied to the updated amount (principal + interest) from the previous year.

Simple Interest

• Simple Interest Formula: PRT/100 (P = Principal, R = Rate of Interest, T = Time).
• Rate of Interest (R) is always in percentage and per annum (per year).
• Time (T) should always be in years. Convert months to years by dividing by 12.
• The "/100" in the formula accounts for the percentage in the rate of interest.
• Amount Formula for Simple Interest: Principal + Interest.
• Direct Amount Formula for Simple Interest: P(1 + RT/100).
• With Simple Interest, the Rate of Interest is always applied to the original principal.
• Alternate way to obtain the amount is to calculate the total return in percentage for the whole period, then apply it to the principle.
• If return (interest) is obtained in percentage , add it to 100 to find the total percentage to be applied to the principle

Example 1: Time Calculation

• Find the time it takes for ₹450 to yield ₹81 as interest at a rate of 4.5% per annum simple interest.
• If a question only mentions "interest" without specifying simple or compound, it defaults to Simple Interest.
• Apply the Simple Interest formula, 81 = (450 * 4.5 * T) / 100, and solve for T.
• Convert 4.5 to 45/10 and simplify to find T = 4 years.

Example 2: Calculating Principle

• Calculate the amount borrowed, given the amount paid after 3 years amounts to ₹10400 at a 10% interest rate.
• Let the principal be P. After 3 years at 10% interest per annum, the amount is ₹10400. Find P.
• Use the amount formula for simple interest A = P(1 + RT/100), equate to 10400, and solve for P.

Compound Interest

• In Compound Interest, the amount after each period becomes the principal for the next period.
• The formulas for amount and compound interest vary based on whether the interest is charged yearly, half-yearly, quarterly, etc.
• Interest Charged Yearly: A = P(1 + R/100)^T
• Interest Charged Half-Yearly: A = P(1 + R/2/100)^(2T)
• Interest Charged Quarterly: A = P(1 + R/4/100)^(4T)
• Interest Charged Monthly: A = P(1 + R/12/100)^(12T)
• To find Compound Interest, subtract the Principle from Amount

Successive Muliplication

• Successive multiplication calculates the yearly increase in amount.
• Find the percentage increase and turn it into a decimal.
• For a value undergoing compound interest at a rate of 20%, the amount can be found by multiplying by 1.2 for each year.
• Once the amount is known, Compound Interest can be calculation by subtracting the principle amount from it.

Equivalent Percentage Rate

• Total Return Formula: A + B + (AB/100)
• When the years are different, the returns must be calculated in stages using the formula A + B + (AB/100), where A is the first Return and B is the second return.

Example 3: Compound Interest with Calculations.

• Calculate the amount for a principle of 10,000 for three years at a rate of 10%.
• To make use of the A + B + (AB/100), substitute all years into the formula, and then use the final result to find the total compounded return

Half-Yearly Compounding

• To make use of different compounding periods, apply the method relevant to the period.
• For example, With half-yearly compounding the principal for one year on 5,000 at a rate of 20%, compounded half-yearly, substitute into the relevant formula.