How do I do this interest rate problem?

Question

You have set up an ordinary annuity that will pay you $650.00 a month for the next 25 years. You will earn interest at a rate of 5.5% compounded monthly. What amount did you invest to accomplish this goal?

Answer 1

You are looking for the present value of the money you invested.

Present Value = ?
Future Value = 0
Payments = 650.00
Interest = 5.5%
Compounding Periods = monthly = 12
Payment Periods = monthly = 12
Number of Payments = 12 x 25 = 300

The formula is:

PV = PMT( [1 - (1+i)^-n] / i )

So plugging our information into the formula we have:

PV = 650( [ 1 - (1 + (0.055/12)^-300 ] / (0.055/12) )
PV = 650( [ 1 - (1.004583333)^-300 ] / 0.004583333 )
PV = 650(0.746365 / 0.004583333)
PV = 105 848.11

Therefore, you invested $105 848.11