# Annuity word problem

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1. Sep 9, 2013

### jackscholar

1. The problem statement, all variables and given/known data

3. Sep 9, 2013

### jackscholar

Would that be used in the present value annuity equation where n=1 like so..
P.V.=5000*(1-(1.055)^-1)/0.055?

4. Sep 9, 2013

### Ray Vickson

Forget about using annuity formulas if you do not fully understand them; just proceed from first principles. For an interest rate of 100r %, the PV of $1 received 1 year from now is 1/(1+r) ($). The future value of $1 in one year from now is (1+r) ($). For n periods in the future, the PV is 1/(1+r)^n and the FV is (1+r)^n. For a stream of payments the PVs and FVs are the sum of the separate PV or FV values of the different payments. You could, if you wanted to, express the FV or PV of a steady stream of payments as the sum of a geometric series and use the corresponding summation formulas, but it is often easier to just do the computations directly, without using any formulas; for example, in spreadsheet computations, the direct approach is easiest (and, in some cases, more accurate!!! because it avoids subtractive roundoff errors).

5. Sep 9, 2013

### Staff: Mentor

No. The $5000 is a single payment paid out 16 years from now. So you don't use the annuity equation. Its present value is simply$5000/(i+1)16. Try that in your solution, and you will see that your results match the "answer".

Chet