Week 05b - QMA 2006S2 (Annuities, Sinking Fund &amp; Loan Amortisation)

# Week 05b - QMA 2006S2 (Annuities, Sinking Fund & Loan Amortisation)

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Jessica Chung & Sri Muhunthan Week 05 QMA PASS | 2006 S1 | Mon, 12-1pm | WEB 251 Questions? Email us: jessica.chung@unsw.edu.au , s.muhunthan@student.unsw.edu.au 1/4 G EOMETRIC P ROGRESSIONS (1 ) 1 k a r S r - = - for r < 1 ( 1) 1 k a r S r - = - for r > 1 A NNUITIES An annuity is: a number of equal payments made at regular intervals over a fixed term O RDINARY A NNUITY An ordinary annuity assumes that regular payments are made at the END of a period. Present Value of an Ordinary Annuity 1 (1 ) n i P R i - ± - + ² ³ = × EXAMPLE What is the present value of a 10-year series of \$1000 monthly payments assuming an interest rate of 7.2% per annum compounding monthly? t = 10 k = 12 r = 7.2% R = \$1000 ( ) 120 7.2% 1 (1 ) 12 \$1000 7.2% 12 \$85,366.57 P - ± - + ´ µ ² ³ = × = Future Value of an Ordinary Annuity (1 ) 1 n n i S R i ± + - ² ³ = × EXAMPLE Calculate the future value of the series of money in the above question. t = 10 k = 12 r = 7.2% R = \$1000 ( ) 120 7.2% (1 ) 1 12 \$1000 7.2% 12 \$175,003.01 S ± + - ´ µ ² ³ = × = A NNUITIES D UE An annuity due assumes that regular payments are made at the BEGINNING of a period. Present Value of an Annuity Due 1 (1 ) (1 ) n R i P r i - ± - + ² ³ = + × EXAMPLE If interest were paid at the beginning of a period, calculate the present value of the above stream of money. t = 10 k = 12 r = 7.2% R = \$1000 ( ) ( ) 120 7.2% \$1000 1 (1 ) 12 7.2% 1 12 7.2% 12 \$85,878.77 P - ± - + ´ µ ² ³ = + × = Future Value of an Annuity Due (1 ) 1 (1 ) n n R i S i i ± + - ² ³ = + × EXAMPLE If the above annuity was an annuity due, calculate the future value of the payment stream. t = 10 k = 12 r = 7.2% R = \$1000 ( ) ( ) 120 7.2% \$1000 (1 ) 1 12 7.2% 1 12 7.2% 12 \$176,053.03 S ± + - ´ µ ² ³ = + × =

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Jessica Chung & Sri Muhunthan Week 05 QMA PASS | 2006 S1 | Mon, 12-1pm | WEB 251 Questions? Email us: jessica.chung@unsw.edu.au , s.muhunthan@student.unsw.edu.au 2/4 S INKING F UND A sinking fund is a fund into which regular payments are made in order to achieve a specific objective in the future (such as to replace a machine or a car). You can think of it as if you were depositing this money into the bank (ie just an ordinary annuity type problem) for a holiday abroad. EXAMPLE:
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## This note was uploaded on 04/02/2012 for the course ECON 1101 taught by Professor Julia during the Three '08 term at University of New South Wales.

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Week 05b - QMA 2006S2 (Annuities, Sinking Fund & Loan Amortisation)

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