Final answer:
To determine the number of periods n for the annuity-immediate, the present value formula is rearranged and the given PV, periodic payment.
Step-by-step explanation:
The question pertains to the calculation of the number of periods n for an annuity-immediate given the present value (PV), the periodic payment, and the nominal interest rate compounded quarterly. The PV of an n-year annuity immediate with a payment of $650 per period is $18,002.97.
Using the given nominal annual interest rate of 3.6% compounded quarterly, the periodic interest rate is 0.9% (3.6% / 4). To find the number of periods n, the following formula is used: PV = R × {(1-(1+i)^{-n})/i. Where: PV is the present value of annuity, R is the periodic payment, i is the periodic interest rate, n is the number of periods.
Rearranging the formula to solve for n, and substituting the given values: n = [-ln(1 - PV × i / R)] / ln(1 + i). By substituting PV= $18,002.97, i=0.009, and R=$650 into the formula, we can calculate the exact value of n, which is the number of periods required for the annuity to reach the present value with the given interest rate.