Jasmine has decided that she wants to build enough retirement wealth that, if invested at 6% per year, will provide her with $3,000 of monthly income for 30 years. To date, she has saved nothing but she still has 25 years until she retires. Jasmine believes that she can earn 6% on her investments until she retires. How much money does she need to contribute per month to reach her goal?
A) $512.93
B) $616.27
C) $722.05
D) $863.49

Question

Quizplus · Accepted Answer

Using the formula for the present value of an annuity, we can calculate the amount Jasmine needs to contribute per month:
PV = PMT x [(1 - (1 / (1 + r)^n)) / r]
PV = present value (amount of retirement wealth needed)
PMT = monthly contribution
r = annual interest rate
n = number of periods (in months)

In this case:
PV = ($3,000/month) x (12 months/year) x (30 years) = $1,080,000
PMT = ?
r = 6% / 12 = 0.5% per month
n = 25 years x 12 months/year = 300 months

Plugging in the values:
$1,080,000 = PMT x [(1 - (1 / (1 + 0.005)^300)) / 0.005]

Solving for PMT, we get:
PMT = $722.05

Therefore, Jasmine needs to contribute $722.05 per month to reach her retirement goal. The correct answer is C.

Jasmine Has Decided That She Wants to Build Enough Retirement