Question

Michelle wants to start her own legal practice 10 years from now. She feels she will need $250,000 in today's dollars. She feels that she can earn 8% on her assets and that inflation will run at 4%. She intends to make the first payment at the end of the year. What will be her first payment?

Answers:                        

A. $17,257

B. $20,972

C. $20,195

D. $21,811

Answer 1

(Nominal) Interest rate on assets = 8%

Inflation rate = 4%

effective interest rate = 1.08/1.04 - 1

=1.038462 -1

= 3.8462%

Future value of annuity = P*[(1+i)^n-1]/(i)

where future value of annuity = 250000

p = recurring deposit (?)

i - effective interest rate(3.8462%)

n - no. of recurring deposits(10 years)

put the value in the formula

250000 = p*[(1+0.038462)^10 -1]/(0.038462)

9615.5 = p*[(1.038462)^10 -1 ]

9615.5 = p*[1.458499 -1]

p = 9615.5 / 0.458499

= 20971.7 or 20972

so the option B is correct.

in case of further clarification required please comment.