krit.club logo

Money - Simple Interest

Grade 5ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Principal (PP): This is the original sum of money borrowed from a bank or invested in a scheme. Think of it as the 'seed money' or the base value from which interest grows. In a visual diagram, this would be the starting bar on a graph before any growth occurs.

•

Interest: This is the extra money paid by the borrower to the lender for using their money, or the profit earned by an investor. Visualize this as a 'bonus' pile of money added to the original amount at the end of the term.

•

Rate of Interest (RR): This is the interest charged on every 100100 units of money for a period of one year, usually expressed as a percentage per annum (p.a.p.a.). On a scale of 100100 units, the Rate represents how many units are added as profit each year.

•

Time (TT): The duration for which the money is borrowed or deposited. In Grade 5, this is typically measured in years. If the time is given in months, visualize a clock or calendar where you must convert those months into a fraction of a year by dividing by 1212.

•

Simple Interest (SISI): A method where interest is calculated only on the original Principal throughout the entire time period. Because the Principal never changes, the interest added each year is identical. On a line graph, SISI shows a constant, straight-line upward trend.

•

Amount (AA): The total money returned at the end of the time period. It is the sum of the Principal and the Simple Interest (A=P+SIA = P + SI). Imagine two blocks—a large block representing the Principal and a smaller block representing the Interest—stacked together to show the total value.

•

Per Annum (p.a.p.a.): This Latin phrase means 'per year'. When you see 10%p.a.10\% p.a., visualize a cycle of 1212 months; at the completion of this full cycle, the interest rate is applied to the principal.

📐Formulae

SI=P×R×T100SI = \frac{P \times R \times T}{100}

A=P+SIA = P + SI

SI=A−PSI = A - P

P=A−SIP = A - SI

P=100×SIR×TP = \frac{100 \times SI}{R \times T}

R=100×SIP×TR = \frac{100 \times SI}{P \times T}

T=100×SIP×RT = \frac{100 \times SI}{P \times R}

💡Examples

Problem 1:

Find the Simple Interest and the total Amount for a Principal of 20002000 at a rate of 5%5\% per annum for 44 years.

Solution:

Given: P=2000P = 2000, R=5R = 5, T=4T = 4 \ Step 1: Calculate Simple Interest using the formula SI=P×R×T100SI = \frac{P \times R \times T}{100} \ SI=2000×5×4100SI = \frac{2000 \times 5 \times 4}{100} \ SI=20×5×4=400SI = 20 \times 5 \times 4 = 400 \ Step 2: Calculate Amount using the formula A=P+SIA = P + SI \ A=2000+400=2400A = 2000 + 400 = 2400 \ Therefore, SI=400SI = 400 and Amount=2400Amount = 2400.

Explanation:

We first identify the variables from the problem. We apply the SISI formula to find the interest earned over 44 years. Finally, we add that interest to the original principal to find the total amount to be paid back.

Problem 2:

At what rate of interest per annum will 50005000 amount to 60006000 in 22 years?

Solution:

Given: P=5000P = 5000, A=6000A = 6000, T=2T = 2 \ Step 1: Find the Simple Interest (SISI) first. \ SI=A−PSI = A - P \ SI=6000−5000=1000SI = 6000 - 5000 = 1000 \ Step 2: Use the Rate formula R=100×SIP×TR = \frac{100 \times SI}{P \times T} \ R=100×10005000×2R = \frac{100 \times 1000}{5000 \times 2} \ R=10000010000=10R = \frac{100000}{10000} = 10 \ Therefore, the Rate of Interest is 10%10\% p.a.

Explanation:

Since we are given the final Amount and the Principal, we must first subtract the Principal from the Amount to find out how much interest was actually earned. Once we have the SISI, we can plug it into the derived formula for Rate (RR).