You deposit $2200 in an account that pays 3% annual interest. After 15 years, you withdraw the money, what is the balance if the interest is compounded quarterly?

so I figure you would get 2650.00 help please

What you probably did was calculated simple interest for 15 years on $1000 and added to $2200 to give $2650.

Compound interest formula are based on the number of periods, n, the interest was compounded.

The interest being compounded 4 times a year, so there are 15*4=60 periods of 3 months each. The corresponding interest rate for each period is therefore r = 3%/4=0.0075.

The formula for the future value using compound interest is:
FV = Principal * (1+r)^n
=2200*1.0075^60
=2200*1.565681
=$3444.50

To calculate the balance after 15 years with quarterly compounding, follow these steps:

Step 1: Convert the annual interest rate to a quarterly interest rate. Since there are 4 quarters in a year, divide the annual interest rate by 4. In this case, the quarterly interest rate would be 3% / 4 = 0.75%.

Step 2: Determine the number of compounding periods. Since interest is compounded quarterly, the number of compounding periods would be 15 years × 4 quarters per year = 60 quarters.

Step 3: Apply the compound interest formula:

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

Where:
A = Final balance (amount after 15 years)
P = Initial deposit ($2200)
r = Quarterly interest rate (0.75% or 0.0075 as a decimal)
n = Number of compounding periods per year (4)
t = Number of years (15)

A = 2200(1 + 0.0075/4)^(4*15)
A = 2200(1 + 0.001875)^(60)
A = 2200(1.001875)^(60)
A ≈ 2200 * 1.141377742606826
A ≈ 2501.03

So the balance after 15 years with quarterly compounding at a 3% annual interest rate is approximately $2501.03.

To calculate the balance after 15 years with quarterly compounding, we need to use the compound interest formula:

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

Where:
A = the final amount (balance) after the specified time period
P = the initial deposit (principal 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

Let's plug in the given values into the formula:
P = $2200 (initial deposit)
r = 0.03 (3% annual interest rate, expressed as a decimal)
n = 4 (quarterly compounding, since there are 4 quarters in a year)
t = 15 (number of years)

A = $2200(1 + 0.03/4)^(4*15)

First, let's simplify the inside bracket:
1 + 0.03/4 = 1.0075

Now, substitute this value back into our formula:
A = $2200(1.0075)^(60)

Using a calculator, raise 1.0075 to the power of 60:
A ≈ $2650.68

So, the balance after 15 years with quarterly compounding would be approximately $2650.68.