SOLUTION: No technology is required for this question. a) Which annuity formula - Present Value or Future Value - more closely resembles the geometric series formula? Explain. b) Why i

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Question 1202634: No technology is required for this question.
a) Which annuity formula - Present Value or Future Value - more closely resembles the geometric series formula? Explain.
b) Why is an annuity an example of a geometric series? Explain.
c) Why can we not model compound interest with the geometric series formula?.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i believe the future value equation closely resembles the geometric series equation.
as an example:
assume 1000 is inveted at the end of each month for 20 years at an interest rate of 10% per year.
the future value of the annuity will be equal to 57274.99949.
the sum of the geometric formula for the same problem will be:
Sn = 1000 * (1 - 1.1^20) / (1 - 1.1) = 57274.99949
they're the same.

answers to your questions:

a) Which annuity formula - Present Value or Future Value - more closely resembles the geometric series formula? Explain.

the future value of an annuity formula most closely resembles the sum of a geometric series formula.

b) Why is an annuity an example of a geometric series? Explain.

they do the same thing.
they both take the annuity and multiiply it by the growth factor.
they then add up the annuity for the numbe of time periods to get the future value.
in the sum of a geometric series formula, A1 is the annuity.

c) Why can we not model compound interest with the geometric series formula?.

we can model compound interest with the geometric series formula.
they're related.
some modifications need to be considered to make them provide the same answer, but they do provide the same answer if the parameters of the formulas are modified correctly.

if you need a more detailed explanation, let me know what more you need.