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?

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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.

Vince Has $35,000 to Purchase an Annuity That Will Provide