Pam and Tim decide to start saving money for their daughter's college education. They open a college savings plan with a 400 initial investment and next month start to make monthly deposits of 100. If the account pays 8.00% compounded monthly, how much will the account be worth after 180 deposits? Be sure to include the initial investment in the computation.
An excel spreadsheet is very helpful for these kinds of calculations.
worth $35,935.41.
To calculate the worth of the account after 180 deposits, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the initial investment is $400, and the monthly deposit is $100. So, the principal amount (P) for the formula would be $400.
The annual interest rate is 8.00%, which needs to be expressed as a decimal. Divide it by 100 to get 0.08.
The interest is compounded monthly, so n = 12 (number of times interest is compounded per year).
Dealing with time is a bit tricky here because the deposits are made monthly, not yearly. We know that there are 180 deposits in total, but we need to find the number of years (t) accurately. Since each deposit is made monthly, we need to divide the total number of deposits by 12 to get the number of years.
t = 180 deposits / 12 deposits per year
t = 15 years
Now, we have all the required information to plug into the formula:
A = $400(1 + 0.08/12)^(12*15)
Let's calculate it step by step:
Step 1: Calculate the value inside parentheses.
(1 + 0.08/12) = 1.0066667
Step 2: Calculate the exponentiation.
(1.0066667)^(12*15) ≈ 2.410677
Step 3: Multiply the principal amount by the calculated value.
A ≈ $400 * 2.410677
Finally, let's find the worth of the account after 180 deposits:
A ≈ $964.27
Therefore, the account will be worth approximately $964.27 after 180 deposits, including the initial investment.