An annuity provides a payment of [tex]x[/tex] at the end of each year for 12 years. The effective annual interest rate is 3.5%. Find [tex]x[/tex] if the present value of this annuity is equal to 7000.

The value of 'x', the annual payment of the annuity, can be found by using the present value formula for an ordinary annuity, rearranging for 'x', and substituting given values.

Explanation:

The student is asking to find the annual payment amount, denoted as 'x', of an annuity given that the present value of the annuity is $7000, it has a term of 12 years, and an effective annual interest rate of 3.5%. This is a Finance or Mathematics related question dealing with the concept of Present Value of an Annuity. We can use the formula for the present value of an ordinary annuity to solve it:

The formula for the present value of an ordinary annuity is: PV = PMT * [(1 - (1 + r)^-n) / r]
The variables in above formula are PV = present value, PMT = annuity payment, r = interest rate (per period), n = number of periods.
In our case, PV=$7000, r=3.5% (or 0.035 in decimal format), n=12, and PMT=? (which we are trying to calculate).
Rearranging the formula to solve for PMT, we get: PMT = PV / [(1 - (1 + r)^-n) / r]
Substitute given values in above formula to find PMT which is your 'x'. This will give you the value of x as the annual payment for this annuity.

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