if you invest 500 dollars in a savings account that pays 8% interest per year, compounded quarterly, how much will you have in the account at the end of 11.6 years?

the time of 11.6 years is unusual in a question when the interest period is in "quarter years"

11.6 years would be 11.6(4) or 46.4 quarters

amount = 500(1.02)^46.4 = 1253.19

To calculate the future value of the investment, you can use the formula for compound interest:

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

Where:
A = the future value of the investment
P = the principal amount (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

In this case, you have the following information:
P = $500
r = 8% = 0.08
n = 4 (compounded quarterly)
t = 11.6 years

Substituting these values into the formula:

A = 500(1 + 0.08/4)^(4 * 11.6)

Now calculate step by step:

Step 1: Calculate the interest rate per compounding period
0.08/4 = 0.02

Step 2: Calculate the total number of compounding periods
4 * 11.6 = 46.4

Step 3: Calculate the future value
A = 500(1 + 0.02)^46.4

To calculate the result, you can use a calculator or spreadsheet software. The future value will be approximately $1,378.05.

Therefore, at the end of 11.6 years, you will have approximately $1,378.05 in the account.