Simple And Compound Interest
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लेसन नोट्स
Simple Interest
- Interest is money added regularly to an original amount; with simple interest, each payment is the same because it is based only on the starting amount.
- To calculate total simple interest: find a percentage (rate) of the starting amount using a multiplier, then multiply by the number of time periods.
- Total balance = starting amount + total interest earned.
- Example: $250 at 4% per year for 6 years → interest per year = 0.04 × 250 = $10, total interest = 10 × 6 = $60, final balance = 250 + 60 = $310.
- To find the interest rate when given total interest: divide total interest by number of years, then find what percentage that is of the original amount.
- Always check if the question asks for the interest earned or the total amount at the end.
Compound Interest
- Compound interest is calculated on the running total, not just the starting amount, so interest is earned on previously earned interest.
- To calculate compound interest, use a multiplier for the percentage increase and apply it repeatedly for each time period.
- For an increase of r% per year, the multiplier is (1 + r/100). Final amount = P × (multiplier)n, where P is the original amount and n is the number of years.
- Example: $1200 at 4% per year for 7 years → multiplier = 1.04, final amount = 1200 × 1.047 ≈ $1579.
- The compound interest formula is: Final balance = P(1 + r/100)n (not given in exam).
- Depreciation uses a multiplier less than 1; e.g., a 15% decrease has multiplier 0.85.
Comparing Simple and Compound Interest
- Simple interest grows linearly; compound interest grows exponentially.
- For the same rate and time, compound interest yields a higher final amount than simple interest (after the first year).
- Over many years, compound interest eventually always gives a greater amount because interest is earned on interest.
- Example: $1000 at 10% compound vs 12% simple: after 4 years, compound = 1000×1.14 = $1464.10, simple = 1000 + 1000×0.12×4 = $1480; after 6 years, compound = $1771.56, simple = $1720.
Solving Problems with Simple Interest
- To find the rate n% when total amount is known: subtract original to get total interest, divide by years to get annual interest, then find percentage of original.
- Example: £9000 invested for 5 years becomes £11700 → total interest = £2700, annual interest = £540, rate = 540/9000 = 0.06 = 6%.
- To find time: use total interest = P × (r/100) × t, solve for t.
- Always round answers as required (e.g., nearest dollar, nearest hundred).
Solving Problems with Compound Interest
- To find the final amount: use multiplier method or formula P(1 + r/100)n.
- To find the number of years to reach a target: use trial and improvement or logarithms (not required at Core level).
- Example: $1750 at 6.5% compound → target $2000: try n=2 → 1750×1.0652 ≈ $1985, n=3 → 1750×1.0653 ≈ $2114, so at least 3 years.
- To find the interest earned: subtract the original amount from the final amount.
- Example: $8400 at 3.5% for 2 years → final = 8400×1.0352 ≈ $8998.29, interest = $8998.29 - $8400 = $598.29.
Common Mistakes and Tips
- Double-check whether the question uses simple or compound interest.
- Ensure you answer the exact question: interest earned or total amount?
- Round answers appropriately (e.g., to the nearest dollar, nearest cent).
- For compound interest, the multiplier is (1 + r/100); for depreciation, it is (1 - r/100).
स्लाइड्स
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प्रैक्टिस सवाल
फ्री प्रीव्यू — 61 में से 8 सवाल। सभी देखने के लिए साइन अप करें।
1.Simple interest is calculated on which amount?
Easy- AThe original amount only
- BThe current balance each year
- CThe total amount at the end
- DThe interest earned each year
2.Ethan invests $6400 at a rate of 2.6% per year simple interest. Calculate the total value of his investment at the end of 3 years.
Easy- A$6899.20
- B$6656
- C$6720
- D$6998.40
3.Jamie invests $12000 at a rate of 5% per year compound interest. Calculate the value of his investment at the end of 3 years.
Medium- A$13891.50
- B$13800
- C$12600
- D$13900
4.Jan invests $800 at a rate of 3% per year simple interest. Calculate the value of her investment at the end of 4 years.
Easy- A$896
- B$824
- C$872
- D$900
5.Sam invests $4500 into a savings account which pays 3.5% compound interest each year. Find the total amount in the account after 6 years.
Medium- A$5531.65
- B$5445
- C$5670
- D$5590
6.Cody invests $1750 in a savings account which pays 6.5% compound interest each year. How many years will it take for the balance to reach at least $2000?
Medium- A3 years
- B2 years
- C4 years
- D5 years
7.Trina invests $16000 at a rate of 5% per year compound interest. Work out the value of her investment at the end of 4 years.
Medium- A$19448.10
- B$19200
- C$16800
- D$20000
8.Gino invests $6000 for 5 years at a rate of 1.2% per year compound interest. Calculate the value of his investment at the end of the 5 years. Give your answer correct to the nearest dollar.
Medium- A$6369
- B$6360
- C$6372
- D$6000
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