Calculating the Accumulated Value of Periodic Deposits
How can we determine the accumulated value of periodic deposits?
Answer:
The accumulated value of periodic deposits is determined by calculating the total future value of all deposits made over a certain period of time, considering the interest rate and compounding frequency.
The formula for the future value of an ordinary annuity is used to calculate the accumulated value of periodic deposits:
FV = PMT x ((1 + r)^n - 1) / r
Where:
FV = Future value of the annuity
PMT = Payment amount (the periodic deposit)
r = Interest rate per period
n = Number of compounding periods
In the given scenario, periodic deposits of $3,500 are made at the beginning of every quarter for 7 years, with an interest rate of 3.25% compounded quarterly.
First, calculate the total number of compounding periods: 7 years x 4 periods/year = 28 periods.
Next, calculate the quarterly interest rate: 3.25% / 4 = 0.8125%.
Using the formula, with PMT = 3,500, r = 0.8125%, and n = 28, we can find the accumulated value of the periodic deposits after 7 years, which is more than 118,576.43.