Your parents have an investment portfolio of $450,000,and they wish to take out cash flows of $60,000 per year as an ordinary annuity.How long will their portfolio last if the portfolio is invested at an annual rate of 4.50%? Use a calculator to determine your answer.
A)8.00 years
B)9.10 years
C)9.35 years
D)10.14 years

Question

Quizplus · Accepted Answer

To find out how long the portfolio will last, we can use the formula for the present value of an ordinary annuity:

PV = (C/r) x (1 - (1+r)^(-n))

where PV is the present value of the annuity, C is the annual cash flow, r is the annual interest rate, and n is the number of periods (in years).

Substituting the given values, we get:

450,000 = (60,000/0.045) x (1 - (1+0.045)^(-n))

Multiplying both sides by (0.045/60,000) and simplifying, we get:

n = -ln(1 - 0.045/60,000 x 450,000)/ln(1+0.045) = 9.35 years

Therefore, the best choice is C.

Your Parents Have an Investment Portfolio of $450,000,and They Wish