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.

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

Answer 2

To determine which option is better, we need to calculate the amount of money Nancy would have at the end of 3 years for each option.

For Option 1:
The formula to calculate compound interest is: A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years

In this case, P = $50,000, r = 5% or 0.05 (compounded yearly), n = 1, and t = 3.
Plugging in these values into the formula, we get: A1 = 50,000(1 + 0.05/1)^(1*3) = 50,000(1.05)^3 = 57,626.25

For Option 2:
Again, using the compound interest formula: A = P(1 + r/n)^(nt)

For this option, P = $50,000, r = 3.5% or 0.035 (compounded monthly), n = 12 (compounded monthly), and t = 3.
Plugging these values into the formula, we get: A2 = 50,000(1 + 0.035/12)^(12*3) = 50,000(1.00291667)^36 = 57,087.13

Now we can compare the two amounts. We subtract the initial investment from the final amounts:
Difference = A1 - P = 57,626.25 - 50,000 = $7,626.25 (for Option 1)
Difference = A2 - P = 57,087.13 - 50,000 = $7,087.13 (for Option 2)

Therefore, Option 1 earns more interest by $7,626.25, not Option 2 earns more interest by $3,581.52.