Determine the effective rate of interest

Question

Over a 10 year period, an original principal of 4500 accumulated to 6875 in an account in which interest was compounded semiannually. Determine the effective rate of interest (rounded to 2 decimal places).

Answer 1

A = p(1+r/n)^nt

 

6875= 4500(1 + r/2)²⁽¹⁰⁾

 

6875/4500 = (1+r/2)²⁰

 

²⁰√(6875/4500) = 1 + r/2

 

²⁰√(6875/4500) - 1 = r/2

 

r = 2[²⁰√(6875/4500) - 1]

 

r = .04283 ≅ 4.28%

Answer 2

4500(1+r)²⁰=6875

20Log(1+r)=Log[6875/4500]=Log(55/36)

r=exp(Log(55/36)/20)=0.0214168=0.022