Answer:
The correct option is b. $6,304.11.
Explanation:
This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where,
FV = Future value or the amount to have on her 60th birthday = $1,000,000
M = Annual payment or amount she needs to invest each year = ?
r = Interest rate = 8%, or 0.08
n = number of years beginning with her 27th birthday and ending on her 60th birthday = 60 - 27 + 1 = 34
Substituting the values into equation (1) and solve for M, we have:
$1,000,000 = M * (((1 + 0,08)^34 - 1) / 0.08)
$1,000,000 = M * 158.626670073155
M = $1,000,000 / 158.626670073155
M = $6,304.11014452251
Rounding to 2 decimal places, we have:
M = $6,304.11
This implies Katie needs to invest $6,304.11 each year to have exactly $1,000,000 by her 60th birthday.
Therefore, the correct option is b. $6,304.11.
