Business Mathematics and Statistics · Class 11 Commerce
Ch 5Annuity — Class 11 Business Mathematics and Statistics, concept-first.
An annuity is a sequence of equal payments made at equal intervals of time. The rent paid every month, a fixed premium paid every year on a life-insurance policy, the equal instalments in which a loan is cleared, and the equal sum a firm sets aside every year to replace a machine are all annuities.
Key concepts
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Annuity — Meaning and Types
An annuity is a series of equal instalments paid at regular intervals under compound interest. An ordinary annuity (annuity immediate) pays at the end of each period; an annuity due pays at the beginning, so every annuit…
Most relevant Q&A
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Chapter contents
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Concept and Types of Annuity
An annuity is a sequence of equal payments made at equal intervals of time. The rent paid every month, a fixed premium paid every year on a life-insurance policy, the equal instalments in which a loan…
Future Value (Amount) of an Ordinary Annuity
The future value (or amount) of an annuity is the total accumulated value of all the payments, together with the compound interest they earn, computed at the time of the last payment.
Present Value of an Ordinary Annuity
The present value of an annuity is the single lump sum, invested today at the same rate of interest, that would be exactly enough to generate all the future annuity payments.
Special Applications — Annuity Due, Deferred Annuity and Perpetuity
Beyond the plain ordinary annuity, three special cases occur often enough in business to be treated on their own.
Sinking Fund
A sinking fund is a fund built up by setting aside an equal sum at regular intervals so that a known amount is available at a future date — typically to replace a worn-out asset, redeem (pay off) a de…
Loan and Overdraft Repayment (Amortisation)
When a loan (or a bank overdraft) is repaid in equal periodic instalments, the process is called amortisation.
Exercises
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- Q9Define an annuity. Explain, with one business example each, the following types: (i) ordinary annuity, (ii) annuity due, (iii) deferred annu…Free
- Q10The present value of a perpetuity of ₹100 per year, the first payment falling due one year from now, at 5% per annum is:\n(a) ₹500\n(b) ₹1,0…Free
- Q11For the same periodic payment, number of periods and interest rate, the future value of an annuity **due** compared with the future value of…Preview
- Q12Distinguish between a sinking fund and the repayment of a loan by equal instalments. In particular, explain why the annual deposit into a si…Preview
More questions
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- Example 1A person deposits ₹5,000 at the end of every year into an account paying 10% per annum compounded annually. What amount will have accumulate…Free
- Example 2₹1,000 is deposited at the **beginning** of each year for 3 years in a fund earning 10% per annum compounded annually. Find the amount at th…Free
- Example 3Find the present value of an annuity of ₹2,000 payable at the end of each year for 3 years, if money is worth 5% per annum compounded annual…Free
- Example 4A television set has a cash price of ₹10,000. A buyer instead agrees to pay for it in 5 equal annual instalments, the first due one year aft…Preview
- Example 5A philanthropist wishes to award a scholarship of ₹600 every year forever from a fund earning 8% per annum. How large must the fund (corpus)…Preview
- Example 6A company must replace a machine costing ₹1,00,000 at the end of 5 years. It decides to build a sinking fund by depositing an equal sum at t…Preview
- Example 7A loan of ₹50,000 is to be repaid in 4 equal annual instalments at 10% per annum compounded annually, the first instalment due one year afte…Preview
- Example 8A trader clears a bank overdraft of ₹20,000 by 5 equal half-yearly instalments, interest being charged at 8% per annum compounded half-yearl…Preview