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.
A. $26,020
B. $34,820
C. $82,000
D. $91,000
E. None of the above
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.
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.