SOLUTION: Use graphical approximation techniques to answer the question. When would an ordinary annuity consisting of quarterly payments of $ 572.62 at 3 % compounded quarterly be worth more

Question 1161502: Use graphical approximation techniques to answer the question. When would an ordinary annuity consisting of quarterly payments of $ 572.62 at 3 % compounded quarterly be worth more than a principal of $ 6900 invested at 5 % simple interest? it is asking for The annuity would be worth more than the principal in approximately ____ years?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
two equations are required.

the first equation is f = p * (1 + r * n)

to graph this equation, let y = f and x = n
when p = 6900 and r = .05/4, the equation for graphing becomes:
y = 6900 * (1 + .05/4 * x)
y represents the value of the equation for specific values of x.

the second equation is:

FUTURE VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
f = (a*((1+r)^n-1))/r
f is the future value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods

to graph this equation, let y = f and x = n
when a = 572.62 and r = .03/4, the equation for graphing becomes:
y = (572.62 * ((1 + .03/4) ^ x - 1)) / (.03/4)
graph both equations and look for the intersection of the two equations.
that's when the value of each is the same.
since the annuity equation is rising faster than the simple interest equation, then the annuity equation will provide a greater value at all values x greater than at the intersection point.

your solution is that the annuity would be worth more than the principal after approximately 13.428 quarters.

since x had to be consistent across both equations, then everything had to be in quarters, rather than years.
in both equations, x represents quarters of a year.

here's the graph.

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