Andy has set up an ordinary annuity to save for his retirement in 16 years. If his semi-annual payments are $250 and the annuity has an annual interest rate of 7.5%, what will be the value of the annuity when he retires?
How do I solve this equation?
What steps do I take to solve it?
Thank You!
don't you have a formula for the future value of an annuity?
250[(1+.075/2)^16-1]
=.8022278066/(.075/2)
=21.39274151
250(21.39274151)
=5348.18
So, would 5348.18 by the answer?
good start, but 16 years means 32 payments.
Oh, okay
So, I would take 250[1+.075/2)^36-1
=.9517958171
.951795171(.07/4)
=50.76244358
650(50.76244358)
=32995.56 and this would be the answer?
To solve this equation and find the value of the annuity when Andy retires, you can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity
P is the periodic payment
r is the interest rate per period (in this case, per semi-annual period)
n is the number of periods
In this case, the periodic payment is $250, the interest rate is 7.5% per year, the number of periods is 16 years, and since the payments are semi-annual, there will be 32 semi-annual periods (16 years * 2 periods per year).
Now, let's plug these values into the formula and calculate the future value:
r (interest rate per period) = 7.5% / 2 = 0.075 / 2 = 0.0375
n (number of periods) = 16 years * 2 periods per year = 32 periods
FV = $250 * [(1 + 0.0375)^32 - 1] / 0.0375
To evaluate this equation, first calculate the value inside the square brackets: (1 + 0.0375)^32 - 1
Now, raise the base (1 + 0.0375) to the power of 32 and subtract 1 from the result.
Next, divide this result by 0.0375.
Finally, multiply this result by $250 to find the future value of the annuity when Andy retires.
I hope this explanation helps you solve the equation and find the value of the annuity.
Oops, I entered it wrong.
I would take
250[1+.075/2)^3-1
the answer would be 14986.93?