Deposits of $1 are made at the beginning of each year for 14 years. The annual effective interest rate is 3.5%. Calculate the accumulated value of the deposits on the date of the last deposit.
To calculate the accumulated value of the deposits, we can use the formula for the future value of an annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value (accumulated value of the deposits)
P = Annual deposit amount
r = Annual interest rate
n = Number of years
In this case, P = $1, r = 3.5% = 0.035, and n = 14.
FV = $1 * [(1 + 0.035)^14 - 1] / 0.035
= $1 * [1.035^14 - 1] / 0.035
= $1 * [1.557407724 - 1] / 0.035
= $1 * 0.557407724 / 0.035
= $0.557407724 / 0.035
≈ $15.92
Therefore, the accumulated value of the deposits on the date of the last deposit is approximately $15.92.
To calculate the accumulated value of the deposits on the date of the last deposit, we can use the formula for the future value of a series of deposits:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value (accumulated value)
P = Principal deposit amount ($1)
r = Annual effective interest rate (3.5% or 0.035)
n = Number of years (14)
Plugging in the values, we get:
FV = 1 * ((1 + 0.035)^14 - 1) / 0.035
Calculating this expression, we find:
FV ≈ 1 * (1.035^14 - 1) / 0.035
FV ≈ 1 * (1.62689420626 - 1) / 0.035
FV ≈ 1 * 0.62689420626 / 0.035
FV ≈ 17.9112617326
Therefore, the accumulated value of the deposits on the date of the last deposit is approximately $17.91.
To calculate the accumulated value of the deposits on the date of the last deposit, we can use the future value of an ordinary annuity formula.
The formula for the future value of an ordinary annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value of the annuity
P = Annual deposit amount
r = Annual interest rate
n = Number of periods
In this case:
P = $1 (annual deposit amount)
r = 3.5% = 0.035 (annual effective interest rate)
n = 14 (number of years)
Plugging these values into the formula, we get:
FV = 1 * [(1 + 0.035)^14 - 1] / 0.035
FV = 1 * [(1.035)^14 - 1] / 0.035
FV = 1 * [1.6072 - 1] / 0.035
FV = 1 * 0.6072 / 0.035
FV ≈ 17.3497
Therefore, the accumulated value of the deposits on the date of the last deposit is approximately $17.35.