Question

Suppose an investment compounds with an annual interest rate of

11.1%. The equation below models a final balance A given principal
P and time t. Use properties of exponents to approximate the
equivalent monthly interest rate. Enter the approximate monthly
rate as a percentage rounded to two decimal places.
A = P (1.111)ª

Answer 1

To approximate the monthly interest rate, we need to use the formula for the annual percentage rate (APR) that takes into account the effect of compounding:

APR = (1 + r/m)^m - 1

where r is the annual interest rate, m is the number of compounding periods per year, and APR is the annual percentage rate.

In this case, r = 11.1% and m = 12 (since there are 12 months in a year). We want to solve for the monthly interest rate, which we can call r_m:

r_m = (1 + r/12)^12 - 1

r_m = (1 + 0.111/12)^12 - 1

r_m = 0.009141

To convert this to a percentage, we multiply by 100:

r_m = 0.9141%

Therefore, the approximate monthly interest rate is 0.9141%, rounded to two decimal places.