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**Unformatted text preview: **effective annual rate (EAR)
• Effective annual interest rate (EAR) defined
as annual growth rate that takes
compounding into account
• The effective annual interest
Calculating the effective annual rate (EAR)
rate
EAR = (1 + Quoted rate/m)m – 1
- m is the # of compounding periods during a
year
• EAR conversion formula accounts for number
of compounding periods, thus effectively
adjusts annualised interest rate for time value
of money
• EAR is the true cost borrowing and lending. e.g. EARs
• Effective annual rate: Cyclone Rentals borrowed $15,550 from a
bank for 3 years. If the quoted rate (APR) is 6.75 per cent, and the
compounding is daily, what is the effective annual rate (EAR)?
m i 0.0675 EAR = 1 + − 1 = 1 +
m
365 = 1.0698 − 1 = 6.98% 365 −1 Slide
46 Few More Maths on Annuity Calculating annuity PMT
• Brian is a Year 9 student. He plans to buy a car in 4 years.
He estimates that the car will cost him $22,000 in 4 years.
How much money should Brian save each year if he wants
to buy the car? Assume his savings account earns 5.65
per cent annually.
m =1 (1 + i )n − 1 FVAn = CF × i 22,000 = CF × 4.351949362 1.05654 − 1 22,000 = CF × 0.0565 22,000
CF =
= $5,055 .21
4.351949362
Slide
48 e.g. Calculating annuity n
Christine wants to accumulate $247,609.95 so that she can purchase an apartment.
She plans to invest $25,000 at the end of each year. If Christine's savings earn
11.4% p.a., how long will it take for her to reach her goal? m=1 (1 + i )n − 1
FVAn = CF × i 1.114n − 1
247,609.95 = 25,000 × 0.114 247,609.95 1.114n − 1 =
25,000
0.114 1.114 n − 1
9.904398 =
0.114 9.904398 × 0.114 = 1.114 n − 1 1.129101372 + 1 = 1.114n 2.129101372 = 1.114 n l og 2.129101372 = n × log1.114
0.328196339
= n = 7 years
Slide
0.04688519
49 0.328196339 = n × 0.04688519 WORKSHOP & OTHER ACTIVITIES Workshop Questions & Problems Chapter 6 Parrino et. al. 2014 Critical Thinking Questions 6.3, 6.4, 6.8, 6.9 Numerical Problems: 6.1, 6.2, 6.4, 6.5, 6.7, 6.9, 6.11, 6.12, 6.13, 6.14, 6.15, 6.16, 6.18, 6.19, 6.21, 6.22, 6.23, 6.25, 6.27, 6.29, 6.31, 6.35...

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