Math Question

Question

A trust company pays 2.3% compounded semiannually on its three-year GIC. For you to prefer an annually compounded GIC of the same maturity, what value must its nominal interest rate exceed? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

The standard compound interest equation is P=A(1+R/N)^(NT), where P is your final amount, P is your initial investment, R is rate (as a decimal, not a percentage), N is the number of times a year it is compounded and T is the time in years.  we are not given an initial investment amount so just use $1.

 

First we calculate how much the semi-annual 3 yr GIC earns:

 

P=1(1+.023/2)^(2*3)

 

P= (1.0115)^6

 

P= 1.07101443105

 

Now us this amount as P and solve for the rate of an annual GIC over 3 years

 

1.07101443105 = 1(1+R/1)^(1*3)

 

1.07101443105 = (1+R)^3   take the cube root and subtract 1

 

R=2.31%