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Week 04b - QMA 2006S2 (Time Value of Money)

Week 04b - QMA 2006S2 (Time Value of Money) - Jessica...

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Unformatted text preview: Jessica Chung & Derek Hui Week 4 QMA PASS | 2006 S2 | Tues, 3-4pm | QUAD G042 Questions? Email us: [email protected] , [email protected] 1/4 TIME VALUE OF MONEY The same numerical amount of money now, yesterday or in the future does not have the same value. Why? Because money can earn interest over time (to compensate for inflation and loss of liquidity such as in a term deposit). SIMPLE INTEREST Total Interest Earned I P R T PRT = × × = Future Value of Simple Interest (1 ) S P i P Prt P rt = + = + = + Present Value of Simple Interest (1 ) S P rt = + & The amount of interest received is the same for all years COMPOUND INTEREST Total Interest Earned I S P =- Future Value of Compound Interest (1 ) 1 n kt A S P r r P k = + & ¡ = + ¢ £ ¤ ¥ Present Value of Compound Interest ( ) (1 ) 1 n kt A S P r S r k = + = + & “Interest on interest” & The amount of interest received is NOT the same for all years. Why? Because investors need to be rewarded for not taking out the interest payment each year. EXAMPLE A \$1000 fixed deposit at 10% pa compounded annually. (i) How much interest is received at the end of the first year? (ii) At the end of the second year? (iii) In total? (iv) How much interest would have been received in total if the interest payment at the end of the first year was taken out? (100,110,210,200) Repeat this example with simple interest. What is your conclusion? (For simple interest – doesn’t matter when you take money out) THE EXPONENTIAL CONSTANT All you need to know is that the symbol is ‘e’ and it is a CONSTANT (e = 2.71828 …) CONTINUOUS COMPOUNDING Future Value of Continuous Compounding A r t S Pe = Total Interest Earned ( 1) A A r t r t I S P Pe P P e =- =- =- Jessica Chung & Derek Hui Week 4 QMA PASS | 2006 S2 | Tues, 3-4pm | QUAD G042 Questions? Email us: [email protected] , [email protected] 2/4 & As the frequency of compounding increases for a given period, the future value approaches a fixed value. This fixed value is approximated by the above formula. TRY IT YOURSELF! \$1000 at 12% pa for 1 year compounded annually. Then try semi-annually, quarterly, monthly and daily, you’ll find that the difference in values becomes smaller and smaller. Hence – it approaches a fixed value. But for this course basically you just plug numbers into the formula. GENERAL NOTATION & ¡¢£¤¥¦£§¨§££©§¨¡§ª«¤¬¦£ª«¡«­ª ¡¢®«¡¦¤¯¦°¡§ª«¤¬¦£ª«¡«­ª¤¡ª±«¡§ª«¤¬¦£ª«¡«­ª®«¡°¤¥®¤©£¯¦£²®«¡¦¤¯³¯¦´¦¯«µ¶·¸¸¹ º¢£©¥µ«¡¤¬°¤¥®¤©£¯¦£²¤¡¦£ª«¡«­ª®«¡¦¤¯­®«¡¶«§¡ £¢ª¤ª§¨£©¥µ«¡¤¬°¤¥®¤©£¯¦£²¤¡¦£ª«¡«­ª®«¡¦¤¯­ ª¢£©¥µ«¡¤¬¶«§¡­ »¢»¡¦£°¦®§¨¤¡®¡«­«£ª´§¨©« ¼¢°¤¥®¤©£¯§¥¤©£ª¤¡¬©ª©¡«´§¨©«³»¡¦£°¦®§¨½ª¤ª§¨¦£ª«¡«­ª¹...
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Week 04b - QMA 2006S2 (Time Value of Money) - Jessica...

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