Question

First Simple Bank pays 6.4 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

$i =0.050713..$     or

$approximately \ 5.0713..\%$

Explanation:

Assume an investment of $1.00

First Simple Bank:

Amount after 6 years = 1 + PRT

= 1 + 1(0.064)(10)  

= 1.64

 

Complex Bank:

$1*(1+i)^{10} = 1.64$

Take 10th root of both sides

$( (1+i)^ {10})*(\frac{1}{10} ) = 1.64^{\frac{1}{10}}$

$1+i = 1.050713..$

$i =0.050713..$

or

$approximately \ 5.0713..\%$