29. Ray Long wants to retire in Arizona when he is 75 years of age. Ray, who is now 60, believes he will nee $200,000 to retire comfortably. To date, he has set aside no retirement money. If he gets an interest of 12 percent compounded semiannually, he will have to invest today: (Use the tables in the handbook)
A. $26,020
B. $34,820
C. $82,000
D. $91,000
E. None of the above
B ($34,820.)
This was in a multi-choice quiz, and after I took it, it showed me the correct answer. I may have not gotten it right, but hopefully another struggling student can benefit from this.
To calculate the amount Ray Long needs to invest today to achieve his retirement goal, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (which is the desired retirement amount of $200,000)
P = the principal investment (which is what Ray needs to invest today)
r = the annual interest rate (12%)
n = the number of times the interest is compounded per year (semiannually, which means twice a year)
t = the number of years (75 - 60 = 15 years)
Now let's solve for P:
A = P(1 + r/n)^(nt)
$200,000 = P(1 + 0.12/2)^(2*15)
$200,000 = P(1 + 0.06)^(30)
$200,000 = P(1.06)^30
To find the value of (1.06)^30, we can use tables in the handbook or a calculator.
(1.06)^30 ≈ 2.136
Now we can solve for P by rearranging the equation:
$200,000 = P * 2.136
P = $200,000 / 2.136
P ≈ $93,542.48
Therefore, Ray needs to invest approximately $93,542.48 today to achieve his retirement goal of $200,000.
None of the answer choices provided match this amount, so the correct answer is E. None of the above.