Given the following table of interest rates: Investment Year Rates (in %) | Port

Question

Given the following table of interest rates: Investment Year Rates (in %) | Portfolio Rates (in %) Calendar Year of Investment y Calendar Year of Portfolio Rates 2000 4.3 4.8 5.1 4.7 4.7 2004 2001 4.4 4.7 4.5 5.1 4.8 2005 2002 4.8 5.2 5.5 5.2 4.9 2006 2003 5.2 4.8 4.6 5 5.6 2007 2004 5.7 6 6.3 5.3 6.4 62 5.8 2005 6.7 4.6 2007 6.9 Shawn deposits 1000 on January 1, 2001 . The interest rate credited in 2003 is equal to 1 % Aaron deposits 1000 on January 1, 2003. The interest rate credited in 2006 is equal to Muhammad deposits 1000 on January 1, 2000. The interest rate credited in 2006 is equal to Emma deposits 1000 on January 1, 2002. The interest rate credited in 2007 is equal to

Explanation / Answer

a.

in 2001, 2 year inteest rate = 4.70%.

So, value of deposit in 2003 = $1,000 × (1 + 4.70%) ^ 2

= $1,000 × 1.09621

= $1,096.21.

Value of deposit in 2003 is $1,096.21.

b.

in 2003, 3 year inteest rate = 4.60%.

So, value of deposit in 2006 = $1,000 × (1 + 4.60%) ^ 3

= $1,000 × 1.14444

= $1,144.45

Value of deposit in 2006 is $1,144.45

c.

6 year interest rate in 2000 = [(1.0470 ^ 4) × (1.06 ^ 2)] ^ (1 / 6) - 1

= [1.3502 ^ (1 / 6)] - 1

= 1.0513 - 1

= 5.13%.

Value of deposit in 2006 = $1,000 × (1 + 5.13%) ^ 6

= $1,000 × 1.3502

= $1,350.20.

Value of deposit in 2006 will be $1,350.20.

d.

5 year interest rate in 2001 = [(1.0510 ^ 4) × (1.0602 )] ^ (1 / 5) - 1

= [1.2936 ^ (1 / 5)] - 1

= 1.0528 - 1

= 5.28%.

Value of deposit in 2006 = $1,000 × (1 + 5.28%) ^ 5

= $1,000 × 1.2936

= $1,293.60

Value of deposit in 2007 will be $1,293.60.

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