TrLrChVFINANCEMATHEMATICS - Dr Raja Latif.Math 131 Summer...

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Dr. Raja Latif.Math 131 Summer 2005. Pg:1 Ch 5 Finance Mathematics 5.1: COMPOUND INTEREST Compound Interest Formula : For an original principal of P, the formula S P 1 r n gives the compound amount S at the end of n interest (or conversion) periods at the periodic rate of r . Rolf 348 Example 47. On her 58 th birthday, a woman invests $15000 in an account that pays 8% compounded quarterly. How much will be in her account when she retires on her 65 th birthday? 1
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Dr. Raja Latif.Math 131 Summer 2005. Pg:2 Solution . S 15000  1.02 28 $26115.36. Rolf349 Example 49. Daniel received a $1000 gift that he deposited in a savings bank that compounded interest quarterly. After 5 years of accumulating interest, the account had grown to $1485.95. What was the annual interest rate of the bank? Solution . 1485.95 10001 r 20 , so 1 r 20 1.48595. 1 r 1.48595 1/20 which is approximately 1.02, r 0.02, so the annual rate is 8%. Example 349Rolf51.Jerri placed $500 in a credit union that compounded interest semiannually. Her account had grown to $633.39 after 4 years. What was the annual interest rate of the credit union? Solution . 633.39 500 1 r 8 , so 1.26678 1 r 8   1.26678 1/8 1 r 2
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Dr. Raja Latif.Math 131 Summer 2005. Pg:3 1 r 1.029993 r 0.029993 which we round to r 0.03, 6% per year. Example 349Rolf53. Which should you choose: a savings account that starts with $6000 and earns interest at 10% compounded semiannually for 10 years or a lump sum of $ 16000 at the end of 10 years? Solution . For $6000 invested for 10 years, S 6000  1.05 20 $15919.79. The lump sum of $16000 is somewhat better. Rolf349 Example 55. In 14 years an investment of $8000 increases to $18000 in an account that pays interest compounded semiannually. Find the annual interest rate. Solution . S 18000, P 8000, n 28 semiannual periods. 3
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Dr. Raja Latif.Math 131 Summer 2005. Pg:4 18000 8000 1 r 28 2.25 1 r 28 2.25 1/28 1 r 1.0294 1 r r 0.0294 per half year. The annual interest rate is 5.88%. Effective Rate : The effective rate r e that is equivalent to a nominal rate of r compounded n times a year is given by r e 1 r n n 1. 292TAN8 Example . Moesha has an Individual Retirement Account (IRA) with a brokerage firm. Her money is invested in a money-market mutual fund that pays interest on a daily basis. Over a 2 -year period in which no deposits or withdrawals were made, her account grew from $4500 to $5268.24. Find the effective rate at which Moesha’s account was earning interest over that period (assuming 365 4
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Dr. Raja Latif.Math 131 Summer 2005. Pg:5 days in a year). Solution . Let r eff denote the required effective rate of interest. We have 5268.24 4500 1 r eff 2   1 r eff 2 1.17072 1 r eff 1.081998 or r eff 0.081998. Therefore, the required effective rate is 8.20% per year.
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