James has set up an ordinary annuity to save for his retirement in 19 years. If his monthly 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?
I am studying for my math final and I do not remember how to do ordinary annuities. I remember that the equation is:
A=R{1+r/m}^mt-1(r/m)
How do I plug this equation in?
Would it start out like,
A= 250(1+.75/12)^mt-1/(r/m)
Thanks
To calculate the value of an ordinary annuity, you can use the formula you mentioned:
A = R * {(1 + r/m)^(mt) - 1} / (r/m)
Let's break down the formula and plug in the given values:
A = value of the annuity
R = monthly payment
r = annual interest rate (as a decimal)
m = number of compounding periods per year
t = number of years
In this case:
R = $250 (monthly payments)
r = 7.5% = 0.075 (annual interest rate)
m = 12 (monthly compounding periods)
t = 19 (years until retirement)
Now we can substitute these values into the formula:
A = 250 * {(1 + 0.075/12)^(12*19) - 1} / (0.075/12)
Simplifying this expression gives you the value of the annuity when James retires.