Final answer:
To find the length of an annuity time period, use the formula for present value of an annuity and solve for the number of years. The length of this annuity time period is approximately 11.26 years.
Step-by-step explanation:
An annuity costs $70,000 today, pays $5,300 a year, and earns a return of 4.5 percent. To determine the length of the annuity time period, we can use the formula for present value of an annuity:
PV = PMT x ((1 - (1+r)^(-n)) / r)
Where PV is the present value (the cost of the annuity), PMT is the annual payment, r is the rate of return (in decimal form), and n is the number of years. Rearranging the formula, we can solve for n:
n = -log(1 - (PV x r) / PMT) / log(1 + r)
Plugging in the values, we get:
n = -log(1 - (70000 x 0.045) / 5300) / log(1 + 0.045)
Solving this equation gives us the length of the annuity time period, which is approximately 11.26 years.