what is the nominal rate capitalized every three years equivalent to an effective annual rate of 4%? 04/23/2024 2:17 p.m.

To find the nominal rate that is capitalized every three years equivalent to an effective annual rate of 4%, we can use the formula:

(1 + i)^n = 1 + r

Where:
i = nominal rate per period
r = effective annual rate
n = number of compounding periods

Given that the effective annual rate is 4% and is equivalent to a nominal rate capitalized every three years, we have r = 0.04 and n = 3 .

Substitute the values into the formula:

(1 + i)^3 = 1 + 0.04

(1 + i)^3 = 1.04

Taking the cube root of both sides:

1 + i = \sqrt[3]{1.04}
1 + i \approx 1.0133

Subtract 1 from both sides to solve for i :

i \approx 0.0133

Therefore, the nominal rate capitalized every three years equivalent to an effective annual rate of 4% is approximately 1.33%.