How much better is the return on a 6% yearly interest rate investment that is compounded 6 times per year as opposed to compounded yearly?

Select one:

a. Between 1.5% and 2.0% better
b. Between 2.0% and 2.5% better
c. Between 2.5% and 3.0% better
d. Between 3.5% and 4.0% better

To determine how much better the return is on a 6% yearly interest rate investment compounded 6 times per year compared to compounded yearly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years

Let's assume we have an initial investment of $1000 and we want to calculate the final amount after 1 year.

For compounding 6 times per year:
A = 1000(1 + 0.06/6)^(6*1)
A = 1000(1 + 0.01)^6
A = 1000(1.01)^6
A ≈ 1061.52

For compounding yearly:
A = 1000(1 + 0.06/1)^(1*1)
A = 1000(1 + 0.06)^1
A ≈ 1060

The difference in return between the two compounding methods is approximately $1.52.

To compare this difference as a percentage, we calculate (1.52 / 1060) * 100 ≈ 0.143%.

Given the answer choices, the closest option is a. Between 1.5% and 2.0% better.

(1+.06/6)^6 / (1+.06)^1 = 1.051

so, ...