George and Barbara will be retiring in four years and would like to buy a lake house.They estimate that they will need $150,000 at the end of four years to buy this house.They want to make four equal annual payments into an account at the end of each year.If they can earn 16% on their money,compounded annually,over the next four years,how much must they invest at the end of each year for the next four years to have accumulated $150,000 by retirement?
A)$25,523
B)$29,606
C)$46,212
D)$43,500
E)$37,500

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity to solve this problem:

FV = PMT x [(1 + r)^n - 1] / r

where:
PMT = the equal annual payments
r = the interest rate per period (16% compounded annually)
n = the number of periods (4 years)

We need to solve for PMT, which gives us:

PMT = FV x r / [(1 + r)^n - 1]
PMT = $150,000 x 0.16 / [(1 + 0.16)^4 - 1]
PMT = $29,606.22

Therefore, George and Barbara need to invest $29,606.22 at the end of each of the next four years to reach their goal of $150,000. The closest answer choice to this value is B).

George and Barbara Will Be Retiring in Four Years and Would