Vince has $35,000 to purchase an annuity that will provide him with equal payments at the end of every three months for the next six years. If the funds earn 8% compounded quarterly, what is the size of the quarterly payments he will receive?

A) $2,335
B) $1,850
C) $3,734
D) $3,324
E) $7,571

The size of the quarterly payments can be calculated using the formula for the present value of an annuity: $PV=PMT\times \left[\frac{1-(1+r{)}^{-n}}{r}\right]$ , where $PV$ is the present value of the annuity (initial investment), $PMT$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. Given that Vince has $35,000 to invest at an 8% annual interest rate compounded quarterly, the quarterly interest rate is $8\%/4=2\%$ , or $0.02$ as a decimal. The total number of quarterly payments over six years is $6\times 4=24$ . Rearranging the formula to solve for $PMT$ gives us $PMT=PV\times \frac{r}{1-(1+r{)}^{-n}}$ . Substituting the given values, we get $PMT=35000\times \frac{0.02}{1-(1+0.02{)}^{-24}}$ , which calculates to approximately $1,850. Thus, the size of the quarterly payments Vince will receive is about $1,850.