The Stockton Bears Baseball Club Deposits $6,000 at the BEGINNING of each 3-month period for 6 years in an account paying 8% interest compounded quarterly. How much will be in the account at the end of the 6-year period?
To calculate the amount in the account at the end of the 6-year period, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the principal amount (deposit)
r = the annual interest rate (as a decimal)
n = the number of times compounded per year
t = the number of years
In this case:
P = $6,000 (deposit at the beginning of each 3-month period)
r = 8% = 0.08 (8% interest rate per year)
n = 4 (compounded quarterly)
t = 6 years
Step 1: Calculate the interest rate per quarter.
The interest rate per quarter is calculated by dividing the annual interest rate by the number of compounding periods per year:
r_per_quarter = r / n = 0.08 / 4 = 0.02
Step 2: Calculate the number of compounding periods.
Since the deposits are made at the beginning of each 3-month period, and there are 4 quarters in a year, the total number of compounding periods is:
n_compounding_periods = n * t = 4 * 6 = 24 quarters
Step 3: Calculate the future value of the account (A).
A = P(1 + r/n)^(nt)
A = $6,000(1 + 0.02)^24
Using a calculator or spreadsheet software, we can find the value of A.
A ≈ $9,981.44
Therefore, at the end of the 6-year period, there will be approximately $9,981.44 in the account.