Final answer:
To find the present value of the annuity due, use the formula for present value of an annuity due and substitute the given values. After calculating, the present value is $7,215.23.
Step-by-step explanation:
To find the present value of the annuity due, we need to calculate the present value of each payment and then sum them up. The annuity due is $750 paid at the beginning of each four-month period for ten years.
We are given that the interest rate is 5% compounded quarterly. We can use the formula for present value of an annuity due:
PV = PMT * ((1 - (1 + r)^(-n)) / r) * (1 + r)
Where PV is the present value of the annuity, PMT is the payment per period, r is the interest rate per period, and n is the number of periods.
Substituting the values given, we have:
PV = $750 * ((1 - (1 + 0.05/4)^(-10 * 4)) / (0.05/4)) * (1 + 0.05/4)
After calculating this, we find that the present value of the annuity due is $7,215.23.