Alyson deposits $500 in the bank for 12 years. The bank offers her a 4% interest rate compounded monthly. How much money will be in her account at the end of the 12 years? (Remember to round your answer to the nearest cent.)
First, we need to find the interest rate expressed as a decimal. Since Alyson will earn 4% interest, the decimal representation of this is 4/100 = 0.04.
Next, we need to find the number of compounding periods. Since Alyson is compounding her interest monthly for 12 years, she will have 12*12 = <<12*12=144>>144 compounding periods.
Now we can use the compound interest formula to find the amount of money Alyson will have in her account at the end of the 12 years:
A = P(1+r/n)^(n*t)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case,
P = $500
r = 0.04
n = 12 (monthly compounding)
t = 12
Plugging these values into the formula, we get:
A = 500(1+0.04/12)^(12*12)
Calculating this expression, we find:
A = $818.51
So, Alyson will have approximately $818.51 in her account at the end of the 12 years.