Annuities Chapter M7 Learning Objectives Understand and apply annuities Distinguish between future and present value of annuities Solve problems involving the future value of an annuity Calculate the present value of an annuity Calculate the periodic payment of a present value annuity (amortisation) Calculate the periodic payment of a future value annuity © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Annuity An annuity is a series of equal payments, often made under contract, paid at equal intervals (e.g. quarterly or monthly) from an agreed date for a specified period of time. For example, loan repayments. An annuity can also be defined as the sum of money that constitutes a periodic payment. For example, weekly payments of rent. Annuity calculations are based on compound interest calculations. © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Examples of annuities Some common examples of annuities are: mortgage or home loan repayments hire purchase repayments insurance premiums body corporate sinking fund lease payments on cars any loan repayments. © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Main types of annuities With a simple annuity, interest is compounded at the same times as the annuity payments. With a general annuity, interest is compounded at times that are either greater or smaller than when the annuity payments are made. © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Types of simple annuities Ordinary annuities The first payment is made at the end of the first period. Most home loans are structured this way. Annuities due The first payment is made at the beginning of the first period. Most leases are this way. Deferred annuities The first payment is deferred for a number of periods. A perpetuity An annuity in which payments continue indefinitely. © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Annuity terms © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Future value of an annuity The value of an annuity at the end of the term. Where: S = future value R = annuity payment per period i = interest rate per period n = number of payments © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Present or discounted value of an annuity The value at the beginning of the initial rent period. Where: A = present value R = annuity payment per period i = interest rate per period n = number of payments © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Amortisation Periodic payments that will discharge a debt. Where: A = present value R = annuity payment per period i = interest rate per period n = number of payments © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Annuity tables Future value annuity tables Present value annuity tables © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher

Sinking funds A fund into which periodic payments are made so as to accumulate a nominated amount of money in a specified period. Where: S = future value R = annuity payment per period i = interest rate per period n = number of payments © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher