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.)

Answer 1

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.