Question

If you start depositing a constant $200 per month in a particular fund, starting next month, your advisor thinks you should have $936,264.05 forty years later. What effective annual rate of return (EAR) is the advisor assuming that the fund will provide?

Answer 1

given about an annuity,

Monthly deposits = $200

amount after t = 40 years FV = $936264.05

So monthly rate on the bond can be calculated on financial calculator using following values:

FV = 936264.05

N = 40*12 = 480

PMT = -200

PV = 0

Compute for I/Y, we get I/Y = 0.75

So, monthly rate required = 0.75%

Effective annual rate = (1 + monthly rate)^12 - 1 = (1+0.0075)^12 - 1 = 9.38%

So, effective annual rate of return (EAR) is the advisor assuming that the fund will provide is 9.38%