An annuity costs $70,000 today,pays $3,500 a year,and earns a return of 4.5 percent.What is the length of the annuity time period?

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an ordinary annuity:

PV = PMT * ((1 - (1 + r)^-n) / r)

where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of years.

Substituting the given values, we have:

$70,000 = $3,500 * ((1 - (1 + 0.045)^-n) / 0.045)

Simplifying and solving for n, we get:

n = ln(1 - (70000/3500)*0.045) / ln(1+0.045)
n = 52.31 years

Therefore, the length of the annuity time period is 52.31 years. So, the best choice is (C).

An Annuity Costs $70,000 Today,pays $3,500 a Year,and Earns a Return