Determine which is the better investment.

6.8% compounded semiannually or 6.6% compounded quarterly?

An easy way to do this is to choose a term of 1 year and $1 amount.

You can then use the formulas.

For the first one:

P(1+r/2)^2 let P = 1 and r = .068

Do you know how to set up the second one?

yes thanks so much :D

To determine which investment is better, we need to compare the values of future amounts of money earned from each investment option. The future value of an investment can be calculated using the formula:

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

Where:
FV = Future Value
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years the money is invested for

Let's calculate the future value of both investments and compare them.

1. 6.8% compounded semiannually:
Principal amount (P) = 1
Annual interest rate (r) = 6.8% = 0.068 (in decimal form)
Number of times compounded per year (n) = 2 (semiannually)
Number of years (t) = 1

Using the formula:

FV = 1(1 + 0.068/2)^(2*1)
FV = 1(1 + 0.034)^2
FV = 1(1.034)^2
FV = 1.070124

The future value of the investment compounded semiannually is approximately 1.070124.

2. 6.6% compounded quarterly:
Principal amount (P) = 1
Annual interest rate (r) = 6.6% = 0.066 (in decimal form)
Number of times compounded per year (n) = 4 (quarterly)
Number of years (t) = 1

Using the formula:

FV = 1(1 + 0.066/4)^(4*1)
FV = 1(1 + 0.0165)^4
FV = 1(1.0165)^4
FV = 1.067457

The future value of the investment compounded quarterly is approximately 1.067457.

Comparing the future values, we can see that the investment compounded semiannually yields a slightly higher future value (1.070124) compared to the investment compounded quarterly (1.067457). Therefore, based on these calculations, the investment with a 6.8% interest rate compounded semiannually would be the better option.