Business Mathematics and Basic Statistics · Class 11 Commerce
Ch 2Compound Interest — Class 11 Business Mathematics and Basic Statistics, concept-first.
In simple interest, interest is calculated only on the original principal for every period of the loan or investment. In compound interest (CI), the interest earned at the end of each compounding period is added back to the principal, and the next period's interest is calculated on this larger amount.
Key concepts
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Finding an Unknown Principal, Rate or Time in Compound Interest
The compound-interest formula relates four quantities — , , (via ) and . Given any three, the fourth can be found: solve for by dividing by ; solve for the rate or the time by recognising as a power of — in this chapter'…
Most relevant Q&A
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Compound Interest — The Idea of Interest on Interest
In simple interest, interest is calculated only on the original principal for every period of the loan or investment.
Compound Interest Compounded Yearly
When interest is compounded yearly, the interest earned at the end of each year is added to the principal before calculating the next year's interest.
Compound Interest Compounded Half-Yearly
When interest is compounded half-yearly (twice a year), the annual rate is halved to get the rate per half-year, and the number of compounding periods is doubled, since there are 2 half-years in every…
Compound Interest Compounded Quarterly
When interest is compounded quarterly (four times a year), the annual rate is divided by 4 and the number of periods is multiplied by 4, since there are 4 quarters in a year. The amount is
Compound Interest Compounded Monthly
When interest is compounded monthly (twelve times a year), the annual rate is divided by 12 and the number of periods is multiplied by 12. The amount is
Comparing Compounding Frequencies at the Same Nominal Rate
For the same nominal annual rate and the same time , more frequent compounding always gives a larger amount.
Exercises
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- Q7₹8,000 amounts to ₹9,261 in 1 year 6 months when compounded half-yearly. Find the rate of interest per annum.Free
- Q8In how many years will ₹5,000 amount to ₹6,050 at 10% per annum, compounded yearly?Free
- Q9Find the compound interest on ₹10,000 for 1 year at 8% per annum, compounded quarterly.Preview
- Q10Find the amount on ₹12,000 for 8 months at 6% per annum, compounded monthly.Preview
- Q11Find the compound interest on ₹10,000 for 3 years at 10% per annum, compounded half-yearly.Preview
More questions
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- Example 1Find the compound interest on ₹10,000 for 2 years at 10% per annum, compounded yearly.Free
- Example 2A sum of ₹8,000 is invested at 10% per annum, compounded half-yearly, for 1 year 6 months. Find the amount and the compound interest.Free
- Example 3Find the amount and compound interest on ₹16,000 for 9 months at 20% per annum, compounded quarterly.Preview
- Example 4Find the amount on ₹10,000 for 4 months at 12% per annum, compounded monthly.Preview
- Example 5₹20,000 is invested for 1 year at 10% per annum. Find the compound interest if it is compounded (a) yearly, (b) half-yearly, and (c) quarter…Preview
- Example 6At what principal will the amount be ₹13,310 in 3 years at 10% per annum, compounded yearly?Preview