Question

If you start depositing a constant $200 per month in a particular fund, starting next month, your advisor thinks you should have $2,022,987.75 forty years later. What effective annual rate of return (EAR) is the advisor assuming that the fund will provide?

Answer 1

Information provided:

Monthly deposit= $200

Time= 40 years*12= 480 months

Future value= $2,022,987.75

The question is solved by first calculating the yield to maturity.

The yield to maturity is computed by entering the below in a financial calculator:

FV= 2,022,987.75

PMT= -200

N= 480

Press the CPT key and I/Y to compute the yield to maturity.

The answer obtained is 0.96.

Therefore, the yield to maturity is 0.96%*12 = 11.52%.

Effective annual rate is calculated using the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1+0.1152/12)^12 - 1

        = 1.1215 - 1

        = 0.1215*100

= 12.15%

Therefore, the effective annual rate is 12.15%.