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# Ch5b

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Unformatted text preview: 1 0 ower Point Presentation designed by Dr. Sylvia C. Hudgins for Finance 323 at ODU 2 Non-Annual Compounding All equations and calculator solutions thus far have All assumed compounding occurs ONCE a year. assumed Example: Deposit \$1,000 at 10% nominal annual interest rate. How much will you have at end of 1 year? ANNUAL COMPOUNDING 0 \$1,000 1 \$1,000(1.1) \$1,100 SEMI-ANNUAL COMPOUNDING 0 \$1,000 6 months \$1,000(1.05) 1 Earn 10%/2=5% each compounding period \$1,050 \$1,050(1.05) \$1,102.50 3 Non-Annual Compounding All equations and calculator solutions thus far have All assumed compounding occurs ONCE a year. assumed When compounding more than once a year, must When adjust formula FV n = i mn PV(1+ m) m = # of compounding periods in a year Example: Deposit \$1,800 at 8% nominal annual interest rate, compounded quarterly. How much will you have at end of 3 years? .08 4•3 FV3 = 1,800(1+ 4 ) 12 = 1,800(1.02) = 1,800(1.2682) = 2,282.84 4 Non-Annual Compounding When compounding more than once a year, the term When Effective Annual Rate (EAR) is useful for comparisons. Effective Effective Annual Rate (EAR) is the interest rate Effective expressed as if it were compounded once per year. expressed EAR = im (1+m) m = # of compounding periods in a year -1 Example: Deposit \$1,800 at 8% nominal annual interest rate, compounded quarterly. What is the EAR? .08 4 (1+ 4 ) - EAR = = .08243 = 8.24% 1 Non-Annual Compounding Compounding period period Year Year Quarter Quarter Month Month Week Week Day Day Hour Hour Minute Minute Number of times Effective compounded annual rate 1 10.00000% 4 10.38129 12 10.47131 52 10.50648 365 10.51558 8,760 10.51703 525,600 10.51709 5 6 Future Value of an Annuity Annuity- string of deposits with constant value and Annuityfixed interval. fixed 0 1 2 \$0 \$100 3 \$100 \$100 \$100(1.08) \$108 \$100(1.08)2 \$116.64 Compute FV3 \$324.64 How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? FVAN = N (1+i) - 1 PMT( i ) 3 = 100( (1+.08) - 1 ) ....
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