Question

Nancy wants to receive the most return on a $50,000 investment. She has two options. Option 1 gives annual interest at 5% compounded yearly. Option 2 gives annual interest at 3.5% compounded monthly.

Which option is better after 3 , and what is the difference in earned interest?



Option 2 earns more interest by $3,581.52.
Option 2 earns more interest by $2,396.13.

Option 1 earns more interest by $3,581.52.
Option 1 earns more interest by $2,396.13.

Answer 1

All you have to do is to compare the effective annual rate.
5% per annum compounded annually = (1.05)^1 = 1.05
3.5% per annum, compounded monthly = (1..00291666..)^12 = 1.035..
clearly the first one gives you more on your return

assuming you meant: Which option is better after 3 years, and what is the difference in earned interest?

clearly option 1 gives you the better return for any period of same time.
option 1 for 3 years = 50000(1.05)^3 = 57881.25
option 2 for 3 years = 50000(1.0029166..)^36 = 55527.04
difference = $2354.21