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.

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