86.5k views
3 votes
What is the effective annual rate for an APR of 17.00 percent compounded monthly?

a) 18.25%
b) 18.39%
c) 18.11%
d) 17.21%
e) 19.31%

User Schummar
by
8.1k points

1 Answer

2 votes

Final answer:

The effective annual rate for an APR of 17.00% compounded monthly is calculated as 18.0939%, which rounds to 18.09%. The closest option given is 18.11%, which is option c).

Step-by-step explanation:

The effective annual rate (EAR) for an APR of 17.00% compounded monthly can be calculated using the formula EAR = (1 + r/n)^(n*t) - 1, where r is the annual rate (in decimal form), n is the number of compounding periods per year, and t is the number of years. In this case, we have an APR of 17.00% (or 0.17 in decimal form) compounded monthly (n=12), and we want to calculate the equivalent EAR for 1 year (t=1).

Applying the values to the formula gives us EAR = (1 + 0.17/12)^(12*1) - 1. Simplifying, we get EAR = (1 + 0.0141667)^12 - 1, which further simplifies to EAR = 1.180939 - 1, or an EAR of 18.0939%. Therefore, the correct effective annual rate is 18.0939%, which we can round to 18.09% when giving a response.

Looking at the provided options, the closest to our calculated EAR is 18.11%, which is option c).

User Stijn Vanpoucke
by
9.0k points