George and Laura will be retiring in four years and would like to buy a holiday house.They estimate that they will need $550,000 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 8% 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 $550,000 by retirement?
A)$137,500
B)$122,056
C)$113,015
D)$131,821

Question

Quizplus · Accepted Answer

To calculate the equal annual payments that George and Laura need to make, we can use the formula for the future value of an annuity:

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

where FV is the future value, PMT is the equal annual payment, r is the annual interest rate, and n is the number of periods.

Plugging in the given values, we get:

$550,000 = PMT x ((1 + 0.08)^4 - 1) / 0.08

Simplifying, we get:

PMT = $122,056

So George and Laura need to make equal annual payments of $122,056 at the end of each of the next four years to accumulate $550,000 by retirement. The answer is therefore B.

George and Laura Will Be Retiring in Four Years and Would