ted Williams made deposits of 500.00 at the end of each year for eight years. the rat is 8% compounded annually. calculate the value of ted's annuity at the end of eight years
amount = 500( 1.08^8 - 1)/.08
= ...
5,318.30
$5,318.30
To calculate the value of an annuity at the end of a specified period, we can use the future value of an ordinary annuity formula.
The formula to calculate the future value of an ordinary annuity is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Periodic Payment (the deposit made at the end of each year)
r = Interest Rate per period
n = Number of periods
Based on the given information, we have:
P = $500.00
r = 8% = 0.08 (converted to decimal)
n = 8
Now, let's substitute the values into the formula and calculate:
FV = 500 * ((1 + 0.08)^8 - 1) / 0.08
FV = 500 * (1.08^8 - 1) / 0.08
FV = 500 * (2.159274 - 1) / 0.08
FV = 500 * 1.159274 / 0.08
FV = 579.637
Therefore, the value of Ted's annuity at the end of eight years is approximately $579.64.