Annuity investment?

Question

How much would you have to invest each month in a annuity earning 6% monthly to earn $50,000 at the end of 30 years?

Answer 1

This uses the same formula as the one about making $12 payments.

FV = PMT[((1 + i)ⁿ - 1) / i]

Where:

FV = Future Value of an Ordinary Annuity = $50,000
PMT = Amount of each payment
i = Interest Rate Per Period = 0.06/12 = 0.005 = .5% per month
n = Number of Periods = 30 years × (12 months/year) = 360 weeks

Again, I'm assuming that you mean "6% annually, compounded monthly", or an effective monthly interest rate of 0.5%.

This time we're solving for PMT instead of FV.

$50,000 = PMT[((1 + 0.005)^(360) - 1) / 0.005]

$50,000 = PMT(1,004.515)

PMT = $50,000/1,004.515 = $49.78

So he'd only have to put in a little less than $50 a month to earn $50k after 30 years.