Pam and Tim decide to start saving money for their daughter's college education. They open a college savings plan (529) with a 500 dollars initial investment and next month start to make monthly deposits of 120 dollars. If the account pays 8% compounded monthly, how much will the account be worth after 180 deposits? Be sure to include the initial investment in the computation.
To calculate the future value of the college savings plan after 180 deposits, we can use the formula for compound interest:
FV = P * (1 + r/n)^(nt)
Where:
FV = future value
P = principal amount (initial investment)
r = annual interest rate (converted to a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount is $500, the annual interest rate is 8% (or 0.08 as a decimal), the interest is compounded monthly, and the time period is 180 deposits divided by 12 months, which is 15 years.
So, let's plug in the values into the formula and calculate the future value:
FV = 500 * (1 + 0.08/12)^(12*15)
First, we need to calculate the value inside the parentheses: (1 + 0.08/12)^(12*15) simplifies to (1 + 0.00666666667)^(180) = (1.00666666667)^(180).
Next, let's calculate (1.00666666667)^(180). Using a calculator or spreadsheet, we find that the value is approximately 3.172.
Now we can substitute the value of (1.00666666667)^(180) back into the formula:
FV = 500 * 3.172
Calculating 500 * 3.172, we find that the future value of the college savings plan after 180 deposits is approximately $1,586.
Therefore, the account will be worth $1,586 after 180 deposits, including the initial investment of $500.