Katie just turned 25 today. By her 60th birthday she would like to have $1,000,000 saved. She plans to invest equal annual payments beginning with her 27th birthday and ending on her 60th birthday. If all invested funds earn 8% annually, how much does she need to invest each year to have exactly $1,000,000 by her 60th birthday? a. $28,571.43
b. $6,304.11
c. $5,803.26
d. $5,344.67

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.