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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: [email protected] 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 = × E XAMPLE 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 = × E XAMPLE 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 = + × E XAMPLE 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 = + × E XAMPLE 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: [email protected] 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. E XAMPLE : Derek wants to establish a fund for his Jag of \$300,000. He needs to pay an equal amount at the end of each quarter for 10 years, the interest rate is 8% p.a. compounded quarterly.
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Week 05b - QMA 2006S2 (Annuities, Sinking Fund & Loan Amortisation)

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