Financial Applications for Functions question

Question

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 1

Hi!

a) The future value formula more closley resembles the geometric series formula by the very factor (1+i) than the present value formula.

b)Annunity is an example of the geometric series, because annuity is essentially a series of equal payments made at the ends of the equal interval of the regular time period which is used in the geometric series. Also another reason is that annuity deals with constant tatio between successive terms the same as in the geometric series.

c) The compound interest is calculated witht this formula: A=p(1+r)^n .........(1)

So initially n equals zero and all the values put in (1), so A=p(1+e)^0

So A=p, so it is considered the 0th year but in the geometric sequence there is no 0th year, thus we can't model the compound interest formula with the geometric series formula.

Hope this helps!