Alice Longtree has decided to invest $400 quarterly for 4 years in an ordinary annuity at 8 %. As her financial adviser, calculate for Alice the total cash value of the annuity at the end of year 4.
i = .08/4 = .02
n = 16
Amount = 400(1.02^16 - 1)/.02
= ...
To calculate the total cash value of the annuity, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value (total cash value)
P = Periodic Payment (amount invested per quarter)
r = Interest Rate per period
n = Number of periods
In this case:
P = $400
r = 8% = 0.08 (converted to decimal)
n = 4 years * 4 quarters per year = 16 quarters
Substituting these values into the formula:
FV = $400 * [(1 + 0.08)^16 - 1] / 0.08
Calculating the expression within the brackets first:
(1 + 0.08)^16 = 1.08^16 ≈ 2.521
Plugging this value into the formula:
FV = $400 * (2.521 - 1) / 0.08
Calculating the expression within the parentheses:
2.521 - 1 = 1.521
Finally, calculating the total cash value:
FV = $400 * 1.521 / 0.08 = $7,608.75
Therefore, the total cash value of the annuity at the end of year 4 is approximately $7,608.75.
To calculate the total cash value of an ordinary annuity, we need to use the formula for the future value of an ordinary annuity. The formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity
P = Amount of money invested per period ($400 in this case)
r = Interest rate per period (8% or 0.08 in decimal form)
n = Number of periods (4 years in this case)
Using this formula, we can plug in the values and calculate:
FV = $400 * [(1 + 0.08)^4 - 1] / 0.08
Calculating this equation, we find:
FV = $400 * [1.36048 - 1] / 0.08
FV = $400 * 0.36048 / 0.08
FV = $180.192 / 0.08
FV = $2,252.40
Therefore, the total cash value of the annuity at the end of year 4 will be $2,252.40.