Question

1. You project that you will need to live off of $4500 a month for 15 years when you retire. If the money can be invested at 5% interest compounded monthly, how much do you need to have at the time of retirement?

Answer 1

From the given information we need to find the present value of given annuity

Pmt = Periodic monthly payment = 4500

i = Mortgage interest rate per period = 5% = 5/100 = 0.05 => 0.05/12 = 0.00416667

when calculation for 15 years then 15 x 12 = 180

n = Number of payments =180

we can use below formula

PV = Pmt x [(1 - 1 / (1 + i)ⁿ)] / i

PV = 4500 x [(1 - 1 / (1 + 0.00416667)¹⁸⁰)] / (0.00416667)

PV = 4500 X [(1-1/(1.00416667)¹⁸⁰)]/(0.00416667)

PV = 4500 X [1-1/(2.1137)]/(0.00416667)

PV = 4500 X [1-0.4731]/(0.00416667)

PV = 4500 X [0.5269]/(0.00416667)

PV = 4500 X 126.4559

PV = 569051.55

So the present value of annuity = $569051.55

So the required amount at the time of retirement we need $569051.55 for monthly we can draw $4500 for 15 years