Anne Thorne deposits $100 at the end of each month into her savings account which pays 6% interest compounded monthly. How much will be in her account at the end of 2 ½ years?

i = .06/12 = .005

n =2.5(12) = 30

amount = 100( 1.005^30 - 1 )/.005
= $3228.00

To calculate the total amount in Anne Thorne's account at the end of 2 ½ years, we need to use the formula for compound interest:

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

Where:
A = the total amount after time t
P = principal amount (initial deposit)
r = annual interest rate (6% in this case, which is written as 0.06)
n = number of times interest is compounded per year (monthly in this case, so n = 12)
t = time in years (2 ½ years, which is written as 2.5 years)

First, let's calculate the total number of deposits made over 2 ½ years. Since Anne makes monthly deposits, we multiply the number of years by 12:

Number of Deposits = 2.5 years * 12 months/year = 30 deposits

Next, let's calculate the total principal amount deposited:

Total Principal Amount = $100/deposit * 30 deposits = $3,000

Now, we can substitute the values into the compound interest formula:

A = $3,000 * (1 + 0.06/12)^(12 * 2.5)

Simplifying the formula:

A = $3,000 * (1 + 0.005)^(30)

Now, we solve for A:

A = $3,000 * (1.005)^(30)

Using a calculator or spreadsheet, we find that (1.005)^30 ≈ 1.1802.

So the final calculation is:

A ≈ $3,000 * 1.1802

Calculating this value gives us approximately:

A ≈ $3,540.60

Therefore, there will be approximately $3,540.60 in Anne Thorne's account at the end of 2 ½ years.

To calculate the amount in Anne Thorne's account at the end of 2 ½ years, we need to calculate the future value of monthly deposits and compounded interest.

Step 1: Calculate the number of months in 2 ½ years.
2 ½ years = 2.5 years
Months = 2.5 years * 12 months/year
Months = 30 months

Step 2: Calculate the future value of monthly deposits using the formula for the future value of an ordinary annuity:

Future Value = P * ((1 + r)^n - 1) / r

Where:
P = Monthly deposit amount = $100
r = Monthly interest rate = 6% / 12 months = 0.005
n = Number of months = 30 months

Future Value = $100 * ((1 + 0.005)^30 - 1) / 0.005
Future Value ≈ $3,572.71 (rounded to the nearest cent)

Therefore, at the end of 2 ½ years, there will be approximately $3,572.71 in Anne Thorne's savings account.